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

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 $(S(M), i*g_{\delta,0})$ is investigated, where $i*g_{\delta,0}$ is a particular type of induced metric $i*g_{\delta,\sigma}$. Finally, an important example is presented which satisfies in main theorem of the paper.