Some Results on Tangent Bundles with Berger Type Deformed Sasaki Metric over Kählerian Manifolds
Let $M$ be a Kählerian manifold equipped with an almost complex structure $J$ and a Riemannian metric $g$, and let $TM$ be its tangent bundle with the Berger type deformed Sasaki metric. In this paper, firstly, we find all forms of Riemannian curvature tensors of $TM$. Secondly, we search the condit...
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| Date: | 2023 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України
2023
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| Subjects: | |
| Online Access: | https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1025 |
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| Journal Title: | Journal of Mathematical Physics, Analysis, Geometry |
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Journal of Mathematical Physics, Analysis, Geometry| Summary: | Let $M$ be a Kählerian manifold equipped with an almost complex structure $J$ and a Riemannian metric $g$, and let $TM$ be its tangent bundle with the Berger type deformed Sasaki metric. In this paper, firstly, we find all forms of Riemannian curvature tensors of $TM$. Secondly, we search the conditions under which a vector field is harmonic with respect to the Berger type deformed Sasaki metric and give some examples of harmonic vector fields. Finally, we study the harmonicity of maps between the Riemannian manifold and the tangent bundle of another Riemannian manifold and vice versa.
Mathematical Subject Classification 2020: 53C07, 53C55, 53A45 |
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