Geometry of the Second-Order Tangent Bundles of Riemannian M

发布时间：2019-05-13 23:22

【摘要】：Let(M,g) be an n-dimensional Riemannian manifold and T~2M be its secondorder tangent bundle equipped with a lift metric g. In this paper, first, the authors construct some Riemannian almost product structures on(T~2M, g) and present some results concerning these structures. Then, they investigate the curvature properties of(T~2M, g).Finally, they study the properties of two metric connections with nonvanishing torsion on(T~2M, g): The H-lift of the Levi-Civita connection of g to T~2M, and the product conjugate connection defined by the Levi-Civita connection of g and an almost product structure.
[Abstract]:Let(M,g) be an n-dimensional Riemannian manifold and T~2M be its secondorder tangent bundle equipped with a lift metric g. In this paper, first, the authors construct some Riemannian almost product structures on(T~2M, g) and present some results concerning these structures. Then, they investigate the curvature properties of(T~2M, g).Finally, they study the properties of two metric connections with nonvanishing torsion on(T~2M, g): The H-lift of the Levi-Civita connection of g to T~2M, and the product conjugate connection defined by the Levi-Civita connection of g and an almost product structure.
【作者单位】： Department
【分类号】：O186.12

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