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Journals / Hagia Sophia Journal of Geometry / 2022 / Cilt: 4 - Sayı: 1

Berger-type Deformed Sasaki Metric and Harmonicity on Tangent Bundles

Abderrahım ZAGANE
Pages
1–16
Publication Date
2022-07-24
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, we introduce the φφ-unit tangent bundle and we also study the harmonicity of the projection map of the φφ-unit tangent bundle.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this article, we present some results concerning the harmonicity on the tangent bundle equipped with the Berger-type deformed Sasaki metric.
📊
Key Findings & Data:We establish necessary and sufficient conditions under which a vector field is harmonic with respect to the Berger-type deformed Sasaki metric and we construct some examples of harmonic vector fields.
💡
Conclusion & Impact:Finally, we introduce the φφ-unit tangent bundle and we also study the harmonicity of the projection map of the φφ-unit tangent bundle.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Tangent bundles · Berger-type deformed Sasaki metric · harmonic maps

Abstract

In this article, we present some results concerning the harmonicity on the tangent bundle equipped with the Berger-type deformed Sasaki metric. We establish necessary and sufficient conditions under which a vector field is harmonic with respect to the Berger-type deformed Sasaki metric and we construct some examples of harmonic vector fields. We also study the harmonicity of a vector field along a map between Riemannian manifolds, the target manifold being anti-paraKähler equipped with a Berger-type deformed Sasaki metric on its tangent bundle. Also, we discuss the harmonicity of the composition of the projection map of the tangent bundle of a Riemannian manifold with a map from this manifold into another Riemannian manifold, the source manifold being anti-paraKähler whose tangent bundle is endowed with a Berger-type deformed Sasaki metric. After that, we study the harmonicity of the identity map on the tangent bundle equipped with the Berger-type deformed Sasaki metric. Finally, we introduce the φφ-unit tangent bundle and we also study the harmonicity of the projection map of the φφ-unit tangent bundle.

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Cite This Article

ZAGANE, A. (2022). Berger-type Deformed Sasaki Metric and Harmonicity on Tangent Bundles. Hagia Sophia Journal of Geometry, Cilt: 4 - Sayı: 1, 1–16. https://ajindex.com/articles/762891

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