Harmonic geometry of structures on tangent bundle

Abstract

In this thesis we will study the harmonicity of vector fields X whom can be seen as maps from M to its tangent bundle TM endowed with a structures that are almost complex or almost paracomplex, such that those structures are compatible with one of the three metrics: Gradient sasaki metric gf, Berger type deformed Sasaki metric gBS and the isotropic Cheeger-Gromoll metric gδ, CG 0 . We will also give conditions under witch maps between two tangents bundle are harmonic and biharmonic.