We establish the links between the lightlike geometry and basics invariants of the associated semi-Riemannian geometry on r-lightlike submanifold and semi-Riemannian constructed from a semi-Riemannian ambient. Then we...We establish the links between the lightlike geometry and basics invariants of the associated semi-Riemannian geometry on r-lightlike submanifold and semi-Riemannian constructed from a semi-Riemannian ambient. Then we establish some basic inequalities, involving the scalar curvature and shape operator on r-lightlike coisotropic submanifold in semi-Riemannian manifold. Equality cases are also discussed.展开更多
We study totally umbilical screen transversal lightlike submanifolds immersed in a semi-Riemannian product manifold and obtain necessary and sufficient conditions for induced connection ▽ on a totally umbilical radic...We study totally umbilical screen transversal lightlike submanifolds immersed in a semi-Riemannian product manifold and obtain necessary and sufficient conditions for induced connection ▽ on a totally umbilical radical screen transversal lightlike submanifold to be metric connection. We prove a theorem which classifies totally umbilical ST-anti-invariant lightlike submanifold immersed in a semi-Riemannian product manifold.展开更多
We determine the limit of the ratio formed by the independent components of the Riemann tensor to the non-zero component as space dimensionality tends to infinity and find it to be 12. Subsequently we use this result ...We determine the limit of the ratio formed by the independent components of the Riemann tensor to the non-zero component as space dimensionality tends to infinity and find it to be 12. Subsequently we use this result in conjunction with Newtonian classical mechanics to show that the ordinary measurable cosmic energy density is given by while the dark energy density is obviously the Legendre transformation dual energy E(D) = 1 -?E(O). The result is in complete agreement with the COBE, WMAP and type 1a supernova measurements.展开更多
In this paper,the authors study gradient Ricci-Harmonic solitons on warped product manifolds.First,they prove triviality results for the potential and warping functions that reach a maximum or a minimum.In order to pr...In this paper,the authors study gradient Ricci-Harmonic solitons on warped product manifolds.First,they prove triviality results for the potential and warping functions that reach a maximum or a minimum.In order to provide nontrivial examples,they consider the base and the fiber conformal to a semi-Euclidean space,which is invariant under the action of a translation group of co-dimension one.This approach allows them to produce infinitely many examples of geodesically complete semi-Riemannian RicciHarmonic solitons not present in the literature.展开更多
文摘We establish the links between the lightlike geometry and basics invariants of the associated semi-Riemannian geometry on r-lightlike submanifold and semi-Riemannian constructed from a semi-Riemannian ambient. Then we establish some basic inequalities, involving the scalar curvature and shape operator on r-lightlike coisotropic submanifold in semi-Riemannian manifold. Equality cases are also discussed.
文摘We study totally umbilical screen transversal lightlike submanifolds immersed in a semi-Riemannian product manifold and obtain necessary and sufficient conditions for induced connection ▽ on a totally umbilical radical screen transversal lightlike submanifold to be metric connection. We prove a theorem which classifies totally umbilical ST-anti-invariant lightlike submanifold immersed in a semi-Riemannian product manifold.
文摘We determine the limit of the ratio formed by the independent components of the Riemann tensor to the non-zero component as space dimensionality tends to infinity and find it to be 12. Subsequently we use this result in conjunction with Newtonian classical mechanics to show that the ordinary measurable cosmic energy density is given by while the dark energy density is obviously the Legendre transformation dual energy E(D) = 1 -?E(O). The result is in complete agreement with the COBE, WMAP and type 1a supernova measurements.
文摘In this paper,the authors study gradient Ricci-Harmonic solitons on warped product manifolds.First,they prove triviality results for the potential and warping functions that reach a maximum or a minimum.In order to provide nontrivial examples,they consider the base and the fiber conformal to a semi-Euclidean space,which is invariant under the action of a translation group of co-dimension one.This approach allows them to produce infinitely many examples of geodesically complete semi-Riemannian RicciHarmonic solitons not present in the literature.
