Let （M, g） be an n-dimensional Riemannian manifold and T2M be its second- order tangent bundle equipped with a lift metric g. In this paper, first, the authors con- struct some Riemannian almost product structures ...Let （M, g） be an n-dimensional Riemannian manifold and T2M be its second- order tangent bundle equipped with a lift metric g. In this paper, first, the authors con- struct some Riemannian almost product structures on （T2M, g） and present some results concerning these structures. Then, they investigate the curvature properties of （T2M, g）. Finally, they study the properties of two metric connections with nonvanishing torsion on （T2M, g： The//-lift of the Levi-Civita connection of g to TaM, and the product conjugate connection defined by the Levi-Civita connection of g and an almost product structure.展开更多
In this paper.we discuss Lagrangian vector field on Kahler manifold and use it to describe and solve some problem in Newtonican and Lagrangian Mechanics on Kahler Manifold.
Let （Mn, g） and （N^n＋1, G） be Riemannian manifolds. Let TMn and TN^n＋1 be the associated tangent bundles. Let f ： （M^n, g） → （N^＋1, G） be an isometrical immersion with g = f^＊G, F = （f, df） ： （TM^n,g...Let （Mn, g） and （N^n＋1, G） be Riemannian manifolds. Let TMn and TN^n＋1 be the associated tangent bundles. Let f ： （M^n, g） → （N^＋1, G） be an isometrical immersion with g = f^＊G, F = （f, df） ： （TM^n,g） → （TN^n＋1, Gs） be the isometrical immersion with g= F＊Gs where （df）x ： TxM → Tf（x）N for any x∈ M is the differential map, and Gs be the Sasaki metric on TN induced from G. This paper deals with the geometry of TM^n as a submanifold of TN^n＋1 by the moving frame method. The authors firstly study the extrinsic geometry of TMn in TN^n＋1. Then the integrability of the induced almost complex structure of TM is discussed.展开更多
Our previous papers introduce topological notions of normal crossings symplectic divisor and variety,show that they are equivalent,in a suitable sense,to the corresponding geometric notions,and establish a topological...Our previous papers introduce topological notions of normal crossings symplectic divisor and variety,show that they are equivalent,in a suitable sense,to the corresponding geometric notions,and establish a topological smoothability criterion for normal crossings symplectic varieties.The present paper constructs a blowup,a complex line bundle,and a logarithmic tangent bundle naturally associated with a normal crossings symplectic divisor and determines the Chern class of the last bundle.These structures have applications in constructions and analysis of various moduli spaces.As a corollary of the Chern class formula for the logarithmic tangent bundle,we refine Aluffi’s formula for the Chern class of the tangent bundle of the blowup at a complete intersection to account for the torsion and extend it to the blowup at the deepest stratum of an arbitrary normal crossings divisor.展开更多
文摘Let （M, g） be an n-dimensional Riemannian manifold and T2M be its second- order tangent bundle equipped with a lift metric g. In this paper, first, the authors con- struct some Riemannian almost product structures on （T2M, g） and present some results concerning these structures. Then, they investigate the curvature properties of （T2M, g）. Finally, they study the properties of two metric connections with nonvanishing torsion on （T2M, g： The//-lift of the Levi-Civita connection of g to TaM, and the product conjugate connection defined by the Levi-Civita connection of g and an almost product structure.
文摘In this paper.we discuss Lagrangian vector field on Kahler manifold and use it to describe and solve some problem in Newtonican and Lagrangian Mechanics on Kahler Manifold.
基金supported by the National Natural Science Foundation of China(No.61473059)the Fundamental Research Funds for the Central University(No.DUT11LK47)
文摘Let （Mn, g） and （N^n＋1, G） be Riemannian manifolds. Let TMn and TN^n＋1 be the associated tangent bundles. Let f ： （M^n, g） → （N^＋1, G） be an isometrical immersion with g = f^＊G, F = （f, df） ： （TM^n,g） → （TN^n＋1, Gs） be the isometrical immersion with g= F＊Gs where （df）x ： TxM → Tf（x）N for any x∈ M is the differential map, and Gs be the Sasaki metric on TN induced from G. This paper deals with the geometry of TM^n as a submanifold of TN^n＋1 by the moving frame method. The authors firstly study the extrinsic geometry of TMn in TN^n＋1. Then the integrability of the induced almost complex structure of TM is discussed.
基金Supported by NSF grants DMS-2003340(F.Tehrani)DMS-1811861(Mclean)DMS-1901979(Zinger)。
文摘Our previous papers introduce topological notions of normal crossings symplectic divisor and variety,show that they are equivalent,in a suitable sense,to the corresponding geometric notions,and establish a topological smoothability criterion for normal crossings symplectic varieties.The present paper constructs a blowup,a complex line bundle,and a logarithmic tangent bundle naturally associated with a normal crossings symplectic divisor and determines the Chern class of the last bundle.These structures have applications in constructions and analysis of various moduli spaces.As a corollary of the Chern class formula for the logarithmic tangent bundle,we refine Aluffi’s formula for the Chern class of the tangent bundle of the blowup at a complete intersection to account for the torsion and extend it to the blowup at the deepest stratum of an arbitrary normal crossings divisor.
