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| Geometry of the Second-Order Tangent Bundles ofRiemannian Manifolds |
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Citation： |
Aydin GEZER,Abdullah MAGDEN.Geometry of the Second-Order Tangent Bundles ofRiemannian Manifolds[J].Chinese Annals of Mathematics B,2017,38(4):985~998 |
| Page view： 2950
Net amount： 1227 |
Authors： |
Aydin GEZER; Abdullah MAGDEN |
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| Abstract： |
Let $(M,g)$ be an $n$-dimensional Riemannian manifold and $T^{2}M$
be its second-order tangent bundle equipped with a lift metric
$\wt{g}$. In this paper, first, the authors construct some
Riemannian almost product structures on $(T^{2}M,\wt{g})$ and
present some results concerning these
structures. Then, they investigate the curvature properties of $(T^{2}M,\wt{%
g}).$ Finally, they study the properties of two metric connections with
nonvanishing torsion on $(T^{2}M,\wt{g})$: The $H$-lift of the
Levi-Civita connection of $g$ to $T^{2}M,$ and the product conjugate
connection defined by the Levi-Civita connection of $\wt{g}$ and an
almost product structure. |
Keywords： |
Almost product structure, Killing vector field, Metric connection, Riemannian metric, Second-order tangent bundle |
Classification： |
53C07, 53C15, 53A45 |
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