Exploring the Properties of f-Harmonic Vector Fields
In this paper, our objective is to explore specific characteristics of $f$-harmonic vector fields. Firstly, we delve into the properties of an $f$-harmonic Killing vector field when it acts as an $f$-harmonic map between a Riemannian manifold denoted as $(M,g)$ and its tangent bundle $(TM,g_{S})$, w...
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| Date: | 2025 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України
2025
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| Subjects: | |
| Online Access: | https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1102 |
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| Journal Title: | Journal of Mathematical Physics, Analysis, Geometry |
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Journal of Mathematical Physics, Analysis, Geometry| Summary: | In this paper, our objective is to explore specific characteristics of $f$-harmonic vector fields. Firstly, we delve into the properties of an $f$-harmonic Killing vector field when it acts as an $f$-harmonic map between a Riemannian manifold denoted as $(M,g)$ and its tangent bundle $(TM,g_{S})$, which is equipped with the Sasaki metric. We emphasize this investigation when $(M,g)$ takes the form of either an Einstein manifold or a space form. Secondly, we study the traits exhibited by an $f$-harmonic vector field between a Riemannian manifold $(M,g)$ and its tangent bundle $TM$ equipped with either a deformed Sasaki metric $g_{DS}$ or a Mus-Sasaki metric $g_{SF}$. Lastly, we conclude this article by providing insightful examples of $f$-harmonic vector fields in the context of the Heisenberg group.
Mathematical Subject Classification 2020: 53C05, 53C07, 58E20 |
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