Aguilar introduced isotropic almost complex structures $J_{\delta , \sigma}$ on the tangent bundle of a Riemannian manifold $(M,g)$. These structures with the Liouville $1$-form define a class of Riemannian metrics $g_{\delta , \sigma}$ on $TM$ which are a generalization of the Sasaki metric. In this paper, the curvature tensors will be calculated and some results on the Einstein tangent bundles and tangent bundles of constant sectional curvature will be achieved. Moreover, it will be proved that $(T\mathbb{R}^n,g_{\delta , 0})$ is an Einstein manifold if and only if $\delta$ is a constant function. 查看全文>>