Metric connection on tangent bundle with Berger-type deformed Sasaki metric

Abstract

Let TM be the tangent bundle over an almost antipara-Hermitian manifold endowed with Berger-type deformed Sasaki metric $^{BS}g$ . In this paper, we introduce the deformed Sasaki metric which Berger-type and study the metric connection of this metric on the tangent bundle. We give some curvature properties of this metric and characterization of projective vector field which preserving the fiber of $(TM,^{BS} g)$. Next, we present some geometricresults concerning them.