GEOMETRY AND CURVATURE ANALYSIS OF THE BERGER-TYPE CHEEGER-GROMOLL METRIC ON TANGENT BUNDLES OVER ANTI-PARAKÄHLER MANIFOLDS

In this paper, we introduce a novel metric known as a Berger-type Cheeger-Gromoll metric on the tangent bundle TM over an anti-paraKähler manifold $(M,\varphi ,g)$. In this paper, we introduce a novel metric known as a Berger-type Cheeger-Gromoll metric on the tangent bundle TM over an anti-paraKähler manifold $\varphi $-unit tangent bundle, which is endowed with the Berger-type Cheeger-Gromoll metric. Within this context, we provide the Levi-Civita connection and detail all forms of the Riemannian curvature tensors associated with this metric.