A NEW CLASS OF RIEMANNIAN METRICS ON TANGENT BUNDLE OF A RIEMANNIAN MANIFOLD

Abstract

The class of isotropic almost complex structures, Jδ,σ , define a class of Riemannian metrics, gδ,σ , on the tangent bundle of a Riemannian manifold which are a generalization of the Sasaki metric. This paper characterizes the metrics gδ,0 using the geometry of tangent bundle. As a by-product, some integrability results will be reported for Jδ,σ .