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Journals / Konuralp Journal of Mathematics / 2019 / Volume: 7 Issue: 2

A Note on Two Classes of $\xi$-Conformally Flat Almost Kenmotsu Manifolds

Dibakar Dey(University of Calcutta)
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Publication Date
2019-10-15
DOI
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AI Summary & Key Takeaways

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

Finally, we give an example to verify our result.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The object of the present paper is to characterize $\xi$-conformally flat $(k,\mu)$-almost Kenmotsu manifolds and $(k,\mu)'$-almost Kenmotsu manifolds.
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Key Findings & Data:Further it is shown that a $(2n+1)$-dimensional $(k,\mu)'$-almost Kenmotsu manifold is $\xi$-conformally flat if and only if it is conformally flat.
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Conclusion & Impact:Finally, we give an example to verify our result.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Almost Kenmotsu manifold · Einstein manifold · Riemannian curvature tensor

Abstract

The object of the present paper is to characterize $\xi$-conformally flat $(k,\mu)$-almost Kenmotsu manifolds and $(k,\mu)'$-almost Kenmotsu manifolds. It is proved that a $(k,\mu)$-almost Kenmotsu manifold is $\xi$-conformally flat if and only if the manifold is an Einstein manifold. Further it is shown that a $(2n+1)$-dimensional $(k,\mu)'$-almost Kenmotsu manifold is $\xi$-conformally flat if and only if it is conformally flat. As a consequence of the main results we obtain several corollaries. Finally, we give an example to verify our result.

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Cite This Article

Dey, D. (2019). A Note on Two Classes of $\xi$-Conformally Flat Almost Kenmotsu Manifolds. Konuralp Journal of Mathematics, Volume: 7 Issue: 2. https://ajindex.com/articles/1521713

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