Notes on some properties of the natural Riemann extension

Authors : Filiz OCAK

Pages : 363-373

Doi:10.31801/cfsuasmas.1067247

View : 27 | Download : 50

Publication Date : 2023-06-23

Article Type : Research Paper

Abstract :Let $insert ignore into journalissuearticles values(M,\\nabla);$ be an $n$-dimensional differentiable manifold with a torsion-free linear connection and $T^{*}M$ its cotangent bundle. In this context we study some properties of the natural Riemann extension insert ignore into journalissuearticles values(M. Sekizawa insert ignore into journalissuearticles values(1987);, O. Kowalski and M. Sekizawa insert ignore into journalissuearticles values(2011);); on the cotangent bundle $T^{*}M$. First, we give an alternative definition of the natural Riemann extension with respect to horizontal and vertical lifts. Secondly, we investigate metric connection for the natural Riemann extension. Finally, we present geodesics on the cotangent bundle $T^{*}M$ endowed with the natural Riemann extension.
Keywords : Vertical and horizontal lift, adapted frame, geodesics, natural Riemann extension, cotangent bundle