GEOMETRY AND CURVATURE ANALYSIS OF THE BERGER-TYPE CHEEGER-GROMOLL METRIC ON TANGENT BUNDLES OVER ANTI-PARAKA<spacing diaeresis>HLER MANIFOLDS

In this paper, we introduce a novel metric known as a Berger-type CheegerGromoll metric on the tangent bundle TM over an anti-paraKa<spacing diaeresis>hler manifold (M, phi, g). This metric is defined as a natural metric with respect to the base metric g on TM. We begin by exploring the properties of the Levi-Civita connection associated with this metric. Subsequently, we compute all the components of the Riemannian curvature tensor and provide an explicit expression for the sectional curvature and the scalar curvature. In the final part of our analysis, we delve into the geometry of the phi- 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.