Communications of the
Korean Mathematical Society CKMS

The class of isotropic almost complex structures, $J_{\delta , \sigma}$, define a class of Riemannian metrics, $g_{\delta , \sigma}$, on the tangent bundle of a Riemannian manifold which are a generalization of the Sasaki metric. This paper characterizes the metrics $g_{\delta , 0}$ using the geometry of tangent bundle. As a by-product, some integrability results will be reported for $J_{\delta , \sigma}$.

Keywords: Einstein manifold, isotropic almost complex structure, integrability, space form, tangent bundle

MSC numbers: Primary 53C25, 53C15