On the geometry of tangent bundle of a hypersurface in R n+1

Abstract

In this paper, tangent bundle TM of the hypersurface M in R n+1 has been studied. For hypersurface M given by immersion f : M → R n+1 , considering the fact that F = df : TM → R 2n+2 is also immersion, TM is treated as a submanifold of R 2n+2 . Firstly, an induced metric which is called rescaled induced metric has been defined on TM, and the Levi-Civita connection has been calculated for this metric. Next, curvature tensors of tangent bundle TM have been obtained. Finally, the orthonormal frame at the point (p, u) ∈ TM has been defined and some curvature properties of such a tangent bundle by means of orthonormal frame for a given point have been investigated.