Sur la géométrie des fibres cotangents

Abstract

In this thesis, we study a new class of natural metrics denoted by f g and called the vertical rescaled metric on the cotangent bundle. We calculate its Levi-Civita connection and Riemannian curvature tensor. Also we present some new properties for bi-f-harmonic map between generalized warped product manifolds, for example we calcul the bi-f-harmonicity of the inclusion maps, the bi-f-harmonicity of the projection maps, and bi-f-harmonicity of the prduct maps with harmonic factor.