| Autor: |
Yanlin Li, Aydin Gezer, Erkan Karakaş |
| Jazyk: |
angličtina |
| Rok vydání: |
2023 |
| Předmět: |
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| Zdroj: |
AIMS Mathematics, Vol 8, Iss 8, Pp 17335-17353 (2023) |
| Druh dokumentu: |
article |
| ISSN: |
2473-6988 |
| DOI: |
10.3934/math.2023886?viewType=HTML |
| Popis: |
Let $ (M, g) $ be an $ n $-dimensional (pseudo-)Riemannian manifold and $ TM $ be its tangent bundle $ TM $ equipped with the complete lift metric $ ^{C}g $. First, we define a Ricci quarter-symmetric metric connection $ \overline{\nabla } $ on the tangent bundle $ TM $ equipped with the complete lift metric $ ^{C}g $. Second, we compute all forms of the curvature tensors of $ \overline{\nabla } $ and study their properties. We also define the mean connection of $ \overline{\nabla } $. Ricci and gradient Ricci solitons are important topics studied extensively lately. Necessary and sufficient conditions for the tangent bundle $ TM $ to become a Ricci soliton and a gradient Ricci soliton concerning $ \overline{\nabla } $ are presented. Finally, we search conditions for the tangent bundle $ TM $ to be locally conformally flat with respect to $ \overline{\nabla } $. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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