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Journals / International Electronic Journal of Geometry / 2026 / Volume: 16 Issue: 1

Rigidity Results On Generalized m-Quasi Einstein Manifolds with Associated Affine Killing Vector Field.

Rahul Poddar(SRI SATHYA SAI INSTITUTE OF HIGHER LEARNING)0000-0002-5671-2774
Balasubramanian Subramanian(SRI SATHYA SAI INSTITUTE OF HIGHER LEARNING)0000-0001-8947-4840
R. Sharma(UNIVERSITY OF NEW HAVEN)0000-0001-5026-8564
Pages
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Publication Date
2023-04-30
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

Finally, we show that the same result holds for a complete non-trivial $m$-quasi Einstein manifold $M$ with finite $m$ and associated affine Killing vector field.

📌 3 Key Takeaways

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Objective & Hypothesis:We study a non-trivial generalized $m$-quasi Einstein manifold $M$ with finite $m$ and associated divergence-free affine Killing vector field, and show that $M$ reduces to an $m$-quasi Einstein manifold.
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Key Findings & Data:In addition, if $M$ is complete, then it splits as the product of a line and an $(n-1)$-dimensional negatively Einstein manifold.
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Conclusion & Impact:Finally, we show that the same result holds for a complete non-trivial $m$-quasi Einstein manifold $M$ with finite $m$ and associated affine Killing vector field.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Generalized $m$-quasi Einstein manifold · affine Killing vector field · Einstein manifold

Abstract

We study a non-trivial generalized $m$-quasi Einstein manifold $M$ with finite $m$ and associated divergence-free affine Killing vector field, and show that $M$ reduces to an $m$-quasi Einstein manifold. In addition, if $M$ is complete, then it splits as the product of a line and an $(n-1)$-dimensional negatively Einstein manifold. Finally, we show that the same result holds for a complete non-trivial $m$-quasi Einstein manifold $M$ with finite $m$ and associated affine Killing vector field.

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Cite This Article

Poddar, R., Subramanian, B., Sharma, R. (2023). Rigidity Results On Generalized m-Quasi Einstein Manifolds with Associated Affine Killing Vector Field.. International Electronic Journal of Geometry, Volume: 16 Issue: 1. https://doi.org/10.36890/iejg.1286128

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