Curvatures of metrics induced by the isotropic almost complex structures

TL;DR

This paper calculates the curvature tensors of Riemannian metrics on tangent bundles induced by isotropic almost complex structures, advancing understanding of their geometric properties.

Contribution

It provides explicit curvature tensor formulas for metrics induced by isotropic almost complex structures on tangent bundles, a novel contribution to differential geometry.

Findings

Curvature tensors are explicitly computed for these metrics.

Results enhance understanding of geometric properties of tangent bundle metrics.

New formulas facilitate further research in complex and Riemannian geometry.

Abstract

Isotropic almost complex structures induce a class of Riemannian metrics on tangent bundle of a Riemannian manifold. In this paper the curvature tensors of these metrics will be calculated.