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Journals / International Electronic Journal of Geometry / 2021 / Cilt: 14 - Sayı: 1

Remarks on Scalar Curvature and Concircular Field Equation

Ramesh SHARMA
Sharief DESHMUKH
Pages
121–124
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

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

Finally, we show that, if a complete connected Riemannian manifold admits a concircular non-isometric vector field leaving the scalar curvature invariant, and the conformal function is special concircular, then the scalar curvature is a constant.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We show that the scalar curvature of a Riemannian manifold $M$ is constant if it satisfies (i) the concircular field equation and $M$ is compact, (ii) the special concircular field equation.
📊
Key Findings & Data:We show that the scalar curvature of a Riemannian manifold $M$ is constant if it satisfies (i) the concircular field equation and $M$ is compact, (ii) the special concircular field equation.
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Conclusion & Impact:Finally, we show that, if a complete connected Riemannian manifold admits a concircular non-isometric vector field leaving the scalar curvature invariant, and the conformal function is special concircular, then the scalar curvature is a constant.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Scalar curvature · concircular vector field · concircular scalar equation

Abstract

We show that the scalar curvature of a Riemannian manifold $M$ is constant if it satisfies (i) the concircular field equation and $M$ is compact, (ii) the special concircular field equation. Finally, we show that, if a complete connected Riemannian manifold admits a concircular non-isometric vector field leaving the scalar curvature invariant, and the conformal function is special concircular, then the scalar curvature is a constant.

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Cite This Article

SHARMA, R., DESHMUKH, S. (2022). Remarks on Scalar Curvature and Concircular Field Equation. International Electronic Journal of Geometry, Cilt: 14 - Sayı: 1, 121–124. https://ajindex.com/articles/539566

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