Note on geodesics of cotangent bundle with Berger-type deformed Sasaki metric over Kählerian manifold
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909103953018880 |
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| author | Zagane, Abderrahim |
| author_facet | Zagane, Abderrahim |
| contents | In this paper, first, we introduce the Berger-type deformed Sasaki metric on the cotangent bundle $T^{\ast}M$ over a Kählerian manifold $(M^{2m}, J, g)$ and investigate the Levi-Civita connection of this metric. Secondly, we present the unit cotangent bundle equipped with Berger-type deformed Sasaki metric, and we investigate the Levi-Civita connection. Finally, we study the geodesics on the cotangent bundle and on unit cotangent bundle with respect to the Berger-type deformed Sasaki metric. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_01060 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Note on geodesics of cotangent bundle with Berger-type deformed Sasaki metric over Kählerian manifold Zagane, Abderrahim Differential Geometry 53C15, 53C22(Primary) 53C05, 53C55 (Secondary) In this paper, first, we introduce the Berger-type deformed Sasaki metric on the cotangent bundle $T^{\ast}M$ over a Kählerian manifold $(M^{2m}, J, g)$ and investigate the Levi-Civita connection of this metric. Secondly, we present the unit cotangent bundle equipped with Berger-type deformed Sasaki metric, and we investigate the Levi-Civita connection. Finally, we study the geodesics on the cotangent bundle and on unit cotangent bundle with respect to the Berger-type deformed Sasaki metric. |
| title | Note on geodesics of cotangent bundle with Berger-type deformed Sasaki metric over Kählerian manifold |
| topic | Differential Geometry 53C15, 53C22(Primary) 53C05, 53C55 (Secondary) |
| url | https://arxiv.org/abs/2303.01060 |