A study concerning berger type deformed sasaki metric on the tangent bundle

Let TM be the tangent bundle over an almost anti-paraHermitian manifold endowed with Berger type deformed Sasaki metric gBS. In this paper,first, we obtain the Levi-Civita connection of this metric and study geodesics on TM. Secondly, we construct some almost anti-paraHermitian structures on TM and search conditions for these structures to be anti-paraKähler and quasi-anti-paraKähler. Finally, we present certain Riemannian curvature properties of (TM, gBS). © Murat Altunbas, Ramazan Simsek, and Aydin Gezer, 2019.