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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Збережено в:
Бібліографічні деталі
Дата:2023
Автори: Gezer, Aydin, Zagane, Abderrahim, Djaa, Nour Elhouda
Формат: Стаття
Мова:English
Опубліковано: Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України 2023
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Онлайн доступ:https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1025
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Назва журналу:Journal of Mathematical Physics, Analysis, Geometry

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Journal of Mathematical Physics, Analysis, Geometry
Опис
Резюме: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