- Communications Faculty of Sciences University Ankara Series A1 Mathematics and Statistics
- Vol: 72 Issue: 2
- Notes on some properties of the natural Riemann extension
Notes on some properties of the natural Riemann extension
Authors : Filiz Ocak
Pages : 363-373
Doi:10.31801/cfsuasmas.1067247
View : 25 | Download : 45
Publication Date : 2023-06-23
Article Type : Research Article
Abstract :Let $(M,\\nabla)$ 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 (M. Sekizawa (1987), O. Kowalski and M. Sekizawa (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