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Dergiler / Hagia Sophia Journal of Geometry / 2026 / Cilt: 4 Sayı: 1

Berger-type Deformed Sasaki Metric and Harmonicity on Tangent Bundles

Abderrahım Zagane(RELIZANE University)0000-0001-9339-3787
Sayfa
1–16
Yayın Tarihi
2022-07-24
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this article, we present some results concerning the harmonicity on the tangent bundle equipped with the Berger-type deformed Sasaki metric.
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Temel Bulgular & Veri: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.
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Sonuç & Katkı:Finally, we introduce the φ φ -unit tangent bundle and we also study the harmonicity of the projection map of the φ φ -unit tangent bundle.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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 φ φ -unit tangent bundle and we also study the harmonicity of the projection map of the φ φ -unit tangent bundle.

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Bu Makaleye Atıf Yap

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/1490445

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