In this article, the properties of the homothetic motions in three-dimensional Lorentz space are investigated. Also, some geometric results between velocity and acceleration vectors of a point in a spatial motion are ...In this article, the properties of the homothetic motions in three-dimensional Lorentz space are investigated. Also, some geometric results between velocity and acceleration vectors of a point in a spatial motion are obtained.展开更多
In this paper we classify cylindrically symmetric static space-times according to their teleparallel homothetic vector fields using direct integration technique. It turns out that the dimensions of the teleparallel ho...In this paper we classify cylindrically symmetric static space-times according to their teleparallel homothetic vector fields using direct integration technique. It turns out that the dimensions of the teleparallel homothetic vector fields are 4, 5, 7 or 11, which are the same in numbers as in general relativity. In case of 4, 5 or 7 proper teleparallel homothetic vector fields exist for the special choice to the space-times. In the case of 11 teleparallel homothetic vector fields the space-time becomes Minkowski with all the zero torsion components. Teleparallel homothetic vector fields in this case are exactly the same as in general relativity. It is important to note that this classification also covers the plane symmetric static space-times.展开更多
In this paper we consider the most general form of non-static cylindrically symmetric space-times in order to study proper teleparallel homothetic vector fields using the direct integration technique and diagonal tetr...In this paper we consider the most general form of non-static cylindrically symmetric space-times in order to study proper teleparallel homothetic vector fields using the direct integration technique and diagonal tetrads. This study also covers static cylindrically symmetric, Bianchi type I, non-static and static plane symmetric space-times as well. Here, we will only discuss the cases which do not fall in the category of static cylindrically symmetric, Bianchi type I, non-static and static plane symmetric space-times. From the above study we show that very special classes of the above space-times yield 6, 7 and 8 teleparallel homothetic vector fields with non-zero torsion.展开更多
Quaternion is a division ring.It is shown that planes passing through the origin can be made a field with the quaternion product in R~3.The Hamiltonian operators help us define the homothetic motions on these planes.N...Quaternion is a division ring.It is shown that planes passing through the origin can be made a field with the quaternion product in R~3.The Hamiltonian operators help us define the homothetic motions on these planes.New characterizations for these motions are investigated.展开更多
The Steiner formula and the mixture area formula given by M(U|¨)ller were expressed under the one-parameter closed planar homothetic motions in the complex sense . Also, using the generalization of Steiner formul...The Steiner formula and the mixture area formula given by M(U|¨)ller were expressed under the one-parameter closed planar homothetic motions in the complex sense . Also, using the generalization of Steiner formula, the result of Holditch theorem for homothetic motions is got. In the case of the homothetic scale h≡1 the results given by M(U|¨)ller are obtained as a special case.展开更多
In this paper we consider the homothetic motion of Lorentzian circle by studying the scalar curvature for the corresponding cyclic surface locally. We prove that if the scalar curvature is constant, then . We describe...In this paper we consider the homothetic motion of Lorentzian circle by studying the scalar curvature for the corresponding cyclic surface locally. We prove that if the scalar curvature is constant, then . We describe the equations that govern such surfaces.展开更多
In this paper, the Steiner area formula and the polar moment of inertia were expressed during one-parameter closed planar homothetic inverse motions in complex plane. The Steiner point was defined when the rotation nu...In this paper, the Steiner area formula and the polar moment of inertia were expressed during one-parameter closed planar homothetic inverse motions in complex plane. The Steiner point was defined when the rotation number was different zero and it was called the Steiner normal when the rotation number was equal to zero. The fixed pole point was given with its components and its relation between Steiner point or Steiner normal was explained. The sagittal motion of a telescopic crane was considered as an example. This motion was described by a double hinge consisting of the fixed control panel of the telescopic crane and the moving arm of the telescopic crane. The theoretical concepts and results were applied for this motion.展开更多
In this study, the kinetic energy formula of the projection curve under 1-parameter closed homothetic motion is expressed and as a result, theorem is given. Also some special cases are given related with that formula.
In this paper, during one-parameter closed planar homothetic direct motions, the formula of kinetic energy is expressed. Then we show the relation between the formula of kinetic energy and the Steiner formula. We inve...In this paper, during one-parameter closed planar homothetic direct motions, the formula of kinetic energy is expressed. Then we show the relation between the formula of kinetic energy and the Steiner formula. We investigate some properties of closed planar homothetic motions. These motions appear between two coordinate systems, fixed and moving (direct motion). Finally, we show how the results can be applied to experimentally measured motions. As an example, we consider a motion of winch in the sagittal direction. We obtain the formula of kinetic energy for the motion of winch during one-parameter closed planar homothetic direct motions.展开更多
In this paper, the kinetic energy formula was expressed during one-parameter closed planar homothetic inverse motions in complex plane. Then the relation between the kinetic energy formula and the Steiner formula was ...In this paper, the kinetic energy formula was expressed during one-parameter closed planar homothetic inverse motions in complex plane. Then the relation between the kinetic energy formula and the Steiner formula was given. As an example the sagittal motion of a telescopic crane was considered. This motion was described by a double hinge consisting of the fixed control panel of telescopic crane and the moving arm of telescopic crane. The results were applied to experimentally measured motion.展开更多
In this paper,we study the(α,β)-metrics of constant flag curvature.We characterize almost regular(α,β)-metrics of constant flag curvature under the condition that β is a homothetic 1-form with respect to a.Furthe...In this paper,we study the(α,β)-metrics of constant flag curvature.We characterize almost regular(α,β)-metrics of constant flag curvature under the condition that β is a homothetic 1-form with respect to a.Furthermore,we prove that if a regular(α,β)-metric is of constant flag curvature and β is a Killing 1-form with constant length,then it must be a Riemannian metric or locally Minkowskian.展开更多
In this note,we investigate conformal Killing vectors(CKVs)of locally rotationally symmetric(LRS)Bianchi type V spacetimes.Subject to some integrability conditions,CKVs up to implicit functions of(t,x)are obtained.Sol...In this note,we investigate conformal Killing vectors(CKVs)of locally rotationally symmetric(LRS)Bianchi type V spacetimes.Subject to some integrability conditions,CKVs up to implicit functions of(t,x)are obtained.Solving these integrability conditions in some particular cases,the CKVs are completely determined,obtaining a classification of LRS Bianchi type V spacetimes.The inheriting conformal Killing vectors of LRS Bianchi type V spacetimes are also discussed.展开更多
Exact self-similar solutions to Einstein’s field equations for the Kantowski-Sachs space-time are determined. The self-similarity property is applied to determine the functional form of the unknown functions that def...Exact self-similar solutions to Einstein’s field equations for the Kantowski-Sachs space-time are determined. The self-similarity property is applied to determine the functional form of the unknown functions that define the gravitational model and to reduce the order of the field equations. The consequences of matter, described by the energy-momentum tensor, are investigated in the case of a perfect fluid. Some physical features and kinematical properties of the obtained model are studied.展开更多
Using a navigation process with the datum(F,V),in which F is a Finsler metric and the smooth tangent vector field V satisfies F(−V(x))>1 everywhere,a Lorentz Finsler metric F˜can be induced.Isoparametric functions ...Using a navigation process with the datum(F,V),in which F is a Finsler metric and the smooth tangent vector field V satisfies F(−V(x))>1 everywhere,a Lorentz Finsler metric F˜can be induced.Isoparametric functions and isoparametric hypersurfaces with or without involving a smooth measure can be defined for F˜.When the vector field V in the navigation datum is homothetic,we prove the local correspondences between isoparametric functions and isoparametric hypersurfaces before and after this navigation process.Using these correspondences,we provide some examples of isoparametric functions and isoparametric hypersurfaces on a Funk space of Lorentz Randers type.展开更多
In this paper,we study the conformal vector fields on Finsler warped product manifolds.We obtain a system of equivalent equations that the conformal vector fields on Finsler warped product manifolds satisfy and comple...In this paper,we study the conformal vector fields on Finsler warped product manifolds.We obtain a system of equivalent equations that the conformal vector fields on Finsler warped product manifolds satisfy and completely characterize conformal vector fields on such manifolds.Further,by solving the equation,we give the classification.And we also give some examples.展开更多
文摘In this article, the properties of the homothetic motions in three-dimensional Lorentz space are investigated. Also, some geometric results between velocity and acceleration vectors of a point in a spatial motion are obtained.
文摘In this paper we classify cylindrically symmetric static space-times according to their teleparallel homothetic vector fields using direct integration technique. It turns out that the dimensions of the teleparallel homothetic vector fields are 4, 5, 7 or 11, which are the same in numbers as in general relativity. In case of 4, 5 or 7 proper teleparallel homothetic vector fields exist for the special choice to the space-times. In the case of 11 teleparallel homothetic vector fields the space-time becomes Minkowski with all the zero torsion components. Teleparallel homothetic vector fields in this case are exactly the same as in general relativity. It is important to note that this classification also covers the plane symmetric static space-times.
基金the National Research FoundationNRF,of South Africa for research funding through two grants
文摘In this paper we consider the most general form of non-static cylindrically symmetric space-times in order to study proper teleparallel homothetic vector fields using the direct integration technique and diagonal tetrads. This study also covers static cylindrically symmetric, Bianchi type I, non-static and static plane symmetric space-times as well. Here, we will only discuss the cases which do not fall in the category of static cylindrically symmetric, Bianchi type I, non-static and static plane symmetric space-times. From the above study we show that very special classes of the above space-times yield 6, 7 and 8 teleparallel homothetic vector fields with non-zero torsion.
文摘Quaternion is a division ring.It is shown that planes passing through the origin can be made a field with the quaternion product in R~3.The Hamiltonian operators help us define the homothetic motions on these planes.New characterizations for these motions are investigated.
文摘The Steiner formula and the mixture area formula given by M(U|¨)ller were expressed under the one-parameter closed planar homothetic motions in the complex sense . Also, using the generalization of Steiner formula, the result of Holditch theorem for homothetic motions is got. In the case of the homothetic scale h≡1 the results given by M(U|¨)ller are obtained as a special case.
文摘In this paper we consider the homothetic motion of Lorentzian circle by studying the scalar curvature for the corresponding cyclic surface locally. We prove that if the scalar curvature is constant, then . We describe the equations that govern such surfaces.
文摘In this paper, the Steiner area formula and the polar moment of inertia were expressed during one-parameter closed planar homothetic inverse motions in complex plane. The Steiner point was defined when the rotation number was different zero and it was called the Steiner normal when the rotation number was equal to zero. The fixed pole point was given with its components and its relation between Steiner point or Steiner normal was explained. The sagittal motion of a telescopic crane was considered as an example. This motion was described by a double hinge consisting of the fixed control panel of the telescopic crane and the moving arm of the telescopic crane. The theoretical concepts and results were applied for this motion.
文摘In this study, the kinetic energy formula of the projection curve under 1-parameter closed homothetic motion is expressed and as a result, theorem is given. Also some special cases are given related with that formula.
文摘In this paper, during one-parameter closed planar homothetic direct motions, the formula of kinetic energy is expressed. Then we show the relation between the formula of kinetic energy and the Steiner formula. We investigate some properties of closed planar homothetic motions. These motions appear between two coordinate systems, fixed and moving (direct motion). Finally, we show how the results can be applied to experimentally measured motions. As an example, we consider a motion of winch in the sagittal direction. We obtain the formula of kinetic energy for the motion of winch during one-parameter closed planar homothetic direct motions.
文摘In this paper, the kinetic energy formula was expressed during one-parameter closed planar homothetic inverse motions in complex plane. Then the relation between the kinetic energy formula and the Steiner formula was given. As an example the sagittal motion of a telescopic crane was considered. This motion was described by a double hinge consisting of the fixed control panel of telescopic crane and the moving arm of telescopic crane. The results were applied to experimentally measured motion.
基金supported by the NationalNatural Science Foundation of China(11871126)the Science Foundation of Chongqing Normal University(17XLB022)。
文摘In this paper,we study the(α,β)-metrics of constant flag curvature.We characterize almost regular(α,β)-metrics of constant flag curvature under the condition that β is a homothetic 1-form with respect to a.Furthermore,we prove that if a regular(α,β)-metric is of constant flag curvature and β is a Killing 1-form with constant length,then it must be a Riemannian metric or locally Minkowskian.
文摘In this note,we investigate conformal Killing vectors(CKVs)of locally rotationally symmetric(LRS)Bianchi type V spacetimes.Subject to some integrability conditions,CKVs up to implicit functions of(t,x)are obtained.Solving these integrability conditions in some particular cases,the CKVs are completely determined,obtaining a classification of LRS Bianchi type V spacetimes.The inheriting conformal Killing vectors of LRS Bianchi type V spacetimes are also discussed.
文摘Exact self-similar solutions to Einstein’s field equations for the Kantowski-Sachs space-time are determined. The self-similarity property is applied to determine the functional form of the unknown functions that define the gravitational model and to reduce the order of the field equations. The consequences of matter, described by the energy-momentum tensor, are investigated in the case of a perfect fluid. Some physical features and kinematical properties of the obtained model are studied.
基金Supported by Beijing Natural Science Foundation(Grant No.1222003)National Natural Science Foundation of China(Grant Nos.12131012,11821101 and 12001007)Natural Science Foundation of Anhui province(Grant Nos.2008085QA03 and 1908085QA03)。
文摘Using a navigation process with the datum(F,V),in which F is a Finsler metric and the smooth tangent vector field V satisfies F(−V(x))>1 everywhere,a Lorentz Finsler metric F˜can be induced.Isoparametric functions and isoparametric hypersurfaces with or without involving a smooth measure can be defined for F˜.When the vector field V in the navigation datum is homothetic,we prove the local correspondences between isoparametric functions and isoparametric hypersurfaces before and after this navigation process.Using these correspondences,we provide some examples of isoparametric functions and isoparametric hypersurfaces on a Funk space of Lorentz Randers type.
基金Supported by National Natural Science Foundation of China(Grant Nos.11961061,11461064,11761069)Natural Science Foundation of Xinjiang Uygur Autonomous Region,China(Grant No.2015211C277)。
文摘In this paper,we study the conformal vector fields on Finsler warped product manifolds.We obtain a system of equivalent equations that the conformal vector fields on Finsler warped product manifolds satisfy and completely characterize conformal vector fields on such manifolds.Further,by solving the equation,we give the classification.And we also give some examples.
