Harmonicity of unit vector fields with respect to a class of Riemannian metrics

Abstract

The isotropic almost complex structures induce a Riemannian metric $g_{\delta ,\sigma }$ on TM, which are the generalized type of Sasakian metric. In this paper, the Levi-Civita connection of $g_{\delta ,\sigma }$ is calculated and the harmonicity of unit vector fields from $(M,g)$ to $(S(M),i\ast g_{\delta ,0})$ is investigated, where $i\ast g_{\delta ,0}$ is a particular type of induced metric $i\ast g_{\delta ,\sigma }$. Finally, an important example is presented which satisfies in main theorem of the paper.