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Journals / Hagia Sophia Journal of Geometry / 2021 / Cilt: 3 - Sayı: 1

On the Geometry $(k,\mu )$-Paracontact Metric Manifold Satisfying Certain Curvature Conditions

Pakize UYGUN
Mehmet ATÇEKEN
Pages
16–22
Publication Date
2021-08-30
DOI
—
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AI Summary & Key Takeaways

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

According the cases, we have classified (k,μk,μ)-paracontact metric manifolds.

📌 3 Key Takeaways

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Objective & Hypothesis:In the present paper, we have studied the curvature tensors of (k,μμ)-paracontact metric manifold satisfying the conditions ˜Z(X,Y)⋅R=0Z~(X,Y)⋅R=0, ˜ZZ~, \ R(X,Y)⋅˜Z=0R(X,Y)⋅Z~=0 and $R(X,Y)\cdot R=0$.
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Key Findings & Data:In the present paper, we have studied the curvature tensors of (k,μμ)-paracontact metric manifold satisfying the conditions ˜Z(X,Y)⋅R=0Z~(X,Y)⋅R=0, ˜ZZ~, \ R(X,Y)⋅˜Z=0R(X,Y)⋅Z~=0 and $R(X,Y)\cdot R=0$.
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Conclusion & Impact:According the cases, we have classified (k,μk,μ)-paracontact metric manifolds.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:($k · \mu$)-paracontact manifold · $\eta$-Einstein manifold

Abstract

In the present paper, we have studied the curvature tensors of (k,μμ)-paracontact metric manifold satisfying the conditions ˜Z(X,Y)⋅R=0Z~(X,Y)⋅R=0, ˜ZZ~, \ R(X,Y)⋅˜Z=0R(X,Y)⋅Z~=0 and $R(X,Y)\cdot R=0$. According the cases, we have classified (k,μk,μ)-paracontact metric manifolds.

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Cite This Article

UYGUN, P., ATÇEKEN, M. (2021). On the Geometry $(k,\mu )$-Paracontact Metric Manifold Satisfying Certain Curvature Conditions. Hagia Sophia Journal of Geometry, Cilt: 3 - Sayı: 1, 16–22. https://ajindex.com/articles/762900

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