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Journals / International Electronic Journal of Geometry / 2020 / Cilt: 13 - Sayı: 1

Harmonic Maps and Torse-Forming Vector Fields

Ahmed Mohammed Cherif
Mustapha Djaa
Pages
87–93
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

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

In this paper, we prove that any harmonic map from a compact orientable Riemannian manifoldwithout boundary (or from complete Riemannian manifold) (M, g) to Riemannian manifold (N, h)is necessarily constant, with (N, h) admitting a torse-forming vector field satisfying some condition.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we prove that any harmonic map from a compact orientable Riemannian manifoldwithout boundary (or from complete Riemannian manifold) (M, g) to Riemannian manifold (N, h)is necessarily constant, with (N, h) admitting a torse-forming vector field satisfying some condition.
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Key Findings & Data:In this paper, we prove that any harmonic map from a compact orientable Riemannian manifoldwithout boundary (or from complete Riemannian manifold) (M, g) to Riemannian manifold (N, h)is necessarily constant, with (N, h) admitting a torse-forming vector field satisfying some condition.
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Conclusion & Impact:In this paper, we prove that any harmonic map from a compact orientable Riemannian manifoldwithout boundary (or from complete Riemannian manifold) (M, g) to Riemannian manifold (N, h)is necessarily constant, with (N, h) admitting a torse-forming vector field satisfying some condition.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Harmonic maps · bi-harmonic maps · torse-forming vector fields

Abstract

In this paper, we prove that any harmonic map from a compact orientable Riemannian manifoldwithout boundary (or from complete Riemannian manifold) (M, g) to Riemannian manifold (N, h)is necessarily constant, with (N, h) admitting a torse-forming vector field satisfying some condition.

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Cite This Article

Cherif, A. M., Djaa, M. (2022). Harmonic Maps and Torse-Forming Vector Fields. International Electronic Journal of Geometry, Cilt: 13 - Sayı: 1, 87–93. https://ajindex.com/articles/539616

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