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.
Vertical and horizontal lift adapted frame geodesics natural Riemann extension cotangent bundle
Birincil Dil | İngilizce |
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Konular | Matematik |
Bölüm | Research Article |
Yazarlar | |
Yayımlanma Tarihi | 23 Haziran 2023 |
Gönderilme Tarihi | 2 Şubat 2022 |
Kabul Tarihi | 27 Kasım 2022 |
Yayımlandığı Sayı | Yıl 2023 Cilt: 72 Sayı: 2 |
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.
This work is licensed under a Creative Commons Attribution 4.0 International License.