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Journals / Hagia Sophia Journal of Geometry / 2026 / Cilt: 3 Sayı: 1

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

Pakize Uygun(TOKAT GAZİOSMANPAŞA ÜNİVERSİTESİ)
Mehmet Atçeken(AKSARAY ÜNİVERSİTESİ, FEN-EDEBİYAT FAKÜLTESİ)0000-0002-1242-4359
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 , μ k,μ )-paracontact metric manifolds.

📌 3 Key Takeaways

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

Abstract

In the present paper, we have studied the curvature tensors of (k, μ μ )-paracontact metric manifold satisfying the conditions ˜ Z ( X , Y ) ⋅ R = 0 Z~(X,Y)⋅R=0 , ˜ Z Z~ , \ R ( X , Y ) ⋅ ˜ Z = 0 R(X,Y)⋅Z~=0 and $R(X,Y)\cdot R=0$. According the cases, we have classified ( k , μ k,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/1490453

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