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Journals / International Electronic Journal of Geometry / 2026 / Volume: 13 Issue: 1

Harmonic Maps and Torse-Forming Vector Fields

Ahmed Mohammed Cherif(Mascara Université)0000-0002-6155-0976
Mustapha Djaa(Centre Universitaire de Relizane)0000-0002-7330-2144
Pages
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Publication Date
2020-01-30
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⚡ TL;DR(Too Long; Didn't Read)

In this paper, we prove that any harmonic map from a compact orientable Riemannian manifold without 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 manifold without 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 manifold without 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 manifold without 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 manifold without 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. (2020). Harmonic Maps and Torse-Forming Vector Fields. International Electronic Journal of Geometry, Volume: 13 Issue: 1. https://doi.org/10.36890/iejg.555344

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