Properties of modified Riemannian extensions

Abstract

Let $M$ be an $n-$dimensional differentiable manifold with a symmetric connection $\nabla$ and $T^{\ast }M$ be its cotangent bundle. In this paper, we study some properties of the modified Riemannian extension on $T^{\ast }M$ defined by means of a symmetric -tensor field $c$ on $M.$ We get the conditions under which $T^{\ast }M$ endowed with the horizontal lift ${}^{H}J$ of an almost complex structure $J$ and with the metric ${\tilde{g}}_{\nabla ,c}$ is a Kähler-Norden manifold. Also curvature properties of the Levi-Civita connection and another metric connection of the metric ${\tilde{g}}_{\nabla ,c}$ are presented.

Cited by in corpus (2)

• Ricci flow on modified Riemann extensions
• Yamabe flow on modified Riemann extension