On the geometry of lift metrics and lift connections on the tangent bundle
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866912513657929728 |
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| author | Peyghan, Esmaeil Seifipour, Davood Blaga, Adara M. |
| author_facet | Peyghan, Esmaeil Seifipour, Davood Blaga, Adara M. |
| contents | We study lift metrics and lift connections on the tangent bundle $TM$ of a Riemannian manifold $(M,g)$. We also investigate the statistical and Codazzi couples of $TM$ and their consequences on the geometry of $M$. Finally, we prove a result on $1$-Stein and Osserman structures on $TM$, whenever $TM$ is equipped with the complete lift connection. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_07202 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On the geometry of lift metrics and lift connections on the tangent bundle Peyghan, Esmaeil Seifipour, Davood Blaga, Adara M. Differential Geometry 53B20, 53C05, 53C15, 53C25 We study lift metrics and lift connections on the tangent bundle $TM$ of a Riemannian manifold $(M,g)$. We also investigate the statistical and Codazzi couples of $TM$ and their consequences on the geometry of $M$. Finally, we prove a result on $1$-Stein and Osserman structures on $TM$, whenever $TM$ is equipped with the complete lift connection. |
| title | On the geometry of lift metrics and lift connections on the tangent bundle |
| topic | Differential Geometry 53B20, 53C05, 53C15, 53C25 |
| url | https://arxiv.org/abs/2112.07202 |