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Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 69 Issue: 1

On generalized Cheeger-Gromoll metric and harmonicity

Abderrahim Zagane(Relizane Univesity)0000-0001-9339-3787
Mustapha Djaa(Relizane University)0000-0002-7330-2144
Reda Kada Ben Otmane(Mascara University)0000-0002-0185-6324
Pages
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Publication Date
2020-06-30
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AI Summary & Key Takeaways

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

We also construct some examples of harmonic vector fields.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we introduce the Generalized Cheeger-Gromoll metric on the tangent bundle TM, as a natural metric on TM.
📊
Key Findings & Data:We establish a necessary and sufficient conditions under which a vector field is harmonic with respect to the Generalized Cheeger-Gromoll metric.
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Conclusion & Impact:We also construct some examples of harmonic vector fields.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Horizontal lift · vertical lift · generalized Cheeger-Gromoll metric

Abstract

In this paper, we introduce the Generalized Cheeger-Gromoll metric on the tangent bundle TM, as a natural metric on TM. We establish a necessary and sufficient conditions under which a vector field is harmonic with respect to the Generalized Cheeger-Gromoll metric. We also construct some examples of harmonic vector fields.

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Cite This Article

Zagane, A., Djaa, M., Otmane, R. K. B. (2020). On generalized Cheeger-Gromoll metric and harmonicity. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 69 Issue: 1. https://doi.org/10.31801/cfsuasmas.487296

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