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Journals / Hacettepe Journal of Mathematics and Statistics / 2020 / Cilt: 49 - Sayı: 6

A note on contact metric manifolds

Sharief Deshmukh
Amira A. Ishan
Pages
2007–2016
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

In this paper, first we obtain several necessary and sufficient conditions for a contact metric manifold to be a K-contact manifold and then it is shown that if the Ricci operator of a complete K-contact manifold satisfies a condition like a Codazzi tensor, then it is necessarily a Sasakian manifold.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, first we obtain several necessary and sufficient conditions for a contact metric manifold to be a K-contact manifold and then it is shown that if the Ricci operator of a complete K-contact manifold satisfies a condition like a Codazzi tensor, then it is necessarily a Sasakian manifold.
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Key Findings & Data:In this paper, first we obtain several necessary and sufficient conditions for a contact metric manifold to be a K-contact manifold and then it is shown that if the Ricci operator of a complete K-contact manifold satisfies a condition like a Codazzi tensor, then it is necessarily a Sasakian manifold.
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Conclusion & Impact:In this paper, first we obtain several necessary and sufficient conditions for a contact metric manifold to be a K-contact manifold and then it is shown that if the Ricci operator of a complete K-contact manifold satisfies a condition like a Codazzi tensor, then it is necessarily a Sasakian manifold.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:contact metric manifolds · K-contact manifolds · Killing vector field

Abstract

In this paper, first we obtain several necessary and sufficient conditions for a contact metric manifold to be a K-contact manifold and then it is shown that if the Ricci operator of a complete K-contact manifold satisfies a condition like a Codazzi tensor, then it is necessarily a Sasakian manifold.

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Cite This Article

Deshmukh, S., Ishan, A. A. (2022). A note on contact metric manifolds. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 6, 2007–2016. https://ajindex.com/articles/529655

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