Geometry of the Second-Order Tangent Bundles of Riemannian Manifolds

Let（M,g） be an n-dimensional Riemannian manifold and T;M 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;M, g） and present some results concerning these structures. Then, they investigate the curvature properties of（T;M, g）.Finally, they study the properties of two metric connections with nonvanishing torsion on（T;M, g）: The H-lift of the Levi-Civita connection of g to T;M, and the product conjugate connection defined by the Levi-Civita connection of g and an almost product structure.