M. Altunbas | Searcharxiv

arXiv2013

On the rescaled Riemannian metric of Cheeger Gromoll type on the cotangent bundle

Let $(M,g)$ be an n-dimensional Riemannian manifold and $T^{*}M$ be its cotangent bundle equipped with a Riemannian metric of Cheeger Gromoll type which rescale the horizontal part by a nonzero differentiable function. The main purpose of the present paper is to discuss curvature properties of $T^{*}M$ and construct almost paracomplex Norden structures on $T^{*}M$. We investigate conditions for these structures to be para-Kähler (paraholomorphic) and quasi-Kähler. Also, some properties of almost paracomplex Norden structures in context of almost product Riemannian manifolds are presented.

math.DG↗

arXiv2013

On the geometry of the rescaled Riemannian metric on tensor bundles of arbitrary type

Let $(M,g)$ be an $n-$dimensional Riemannian manifold and $T_{1}^{1}(M)$ be its $(1,1)-$tensor bundle equipped with the rescaled Sasaki type metric $% ^{S}g_{f}$ which rescale the horizontal part by a nonzero differentiable function $f$. In the present paper, we discuss curvature properties of the Levi-Civita connection and another metric connection of $T_{1}^{1}(M)$. We construct almost paracomplex Norden structures on $T_{1}^{1}(M)$ and investigate conditions for these structures to be para-Kähler (paraholomorphic) and quasi-Kähler. Also, some properties of almost paracomplex Norden structures in context of almost product Riemannian manifolds are presented. Finally we introduce the rescaled Sasaki type metric $^{S}g_{f}$ on the $(p,q)-$\ tensor bundle and characterize the geodesics on the $(p,q)$-tensor bundle with respect to the Levi-Civita connection of \textit{${}$}$^{S}g_{f}$ and another metric connection of \textit{${}$}$^{S}g_{f}.$

math.DG↗