On the tangent bundle of a hypersurface in a Riemannian manifold

Abstract

Let (M n , g) and (N n+1 , G) be Riemannian manifolds. Let T M n and T N n+1 be the associated tangent bundles. Let f :for any x ∈ M is the differential map, and Gs be the Sasaki metric on T N induced from G. This paper deals with the geometry of T M n as a submanifold of T N n+1 by the moving frame method. The authors firstly study the extrinsic geometry of T M n in T N n+1 . Then the integrability of the induced almost complex structure of T M is discussed.