ON THE GEOMETRY OF THE RESCALED RIEMANNIAN METRIC ON TENSOR BUNDLES OF ARBITRARY TYPE

Let (M, g) be an n-dimensional Riemannian manifold and T-1(1) (M) be its (1, 1)-tensor bundle equipped with the rescaled Sasaki type metric (s)g(f) which rescale the horizontal part by a non-zero differentiable function f. In the present paper, we discuss curvature properties of the Levi-Civita connection and another metric connection of T-1(1) (M). We construct almost product Riemannian structures on T-1(1)(M) and investigate conditions for these structures to be locally decomposable. Also, some applications concerning with these almost product Riemannian structures on T-1(1)(M) are presented. Finally we introduce the rescaled Sasaki type metric (s)g(f) on the (p, q)-tensor bundle and characterize the geodesics on the (p, q)-tensor bundle with respect to the Levi-Civita connection and another metric connection of (s)g(f).