| 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. |
