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Journals / Turkish Journal of Mathematics and Computer Science / 2026 / Volume: 15 Issue: 1

On $(k,\mu )$-Paracontact Manifold Satisfying Some Curvature Conditions

Pakize Uygun(TOKAT GAZİOSMANPAŞA ÜNİVERSİTESİ)0000-0001-8226-4269
Mehmet Atçeken(AKSARAY ÜNİVERSİTESİ, FEN-EDEBİYAT FAKÜLTESİ)0000-0002-1242-4359
Pages
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Publication Date
2023-06-30
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

Also we researched conformally flat and $\phi $-conformally flat a $(k,\mu )-$paracontact metric manifolds.

📌 3 Key Takeaways

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Objective & Hypothesis:In this work, we studied the curvature tensors of (k,$\mu$) satisfying the conditions $\widetilde{Z}(\xi ,\alpha _{3})\cdot P=0$, $\widetilde{Z}(\xi ,\alpha _{3})\cdot S=0$, $R(\xi ,\alpha _{3})\cdot P=0$, $R(\xi ,\alpha _{3})\cdot S=0$ and $P\cdot C=0$.
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Key Findings & Data:Besides this, we classify $(k,\mu)$-paracontact manifolds.
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Conclusion & Impact:Also we researched conformally flat and $\phi $-conformally flat a $(k,\mu )-$paracontact metric manifolds.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:$(k · \mu)$-Paracontact manifold · Einstein manifold

Abstract

In this work, we studied the curvature tensors of (k,$\mu$) satisfying the conditions $\widetilde{Z}(\xi ,\alpha _{3})\cdot P=0$, $\widetilde{Z}(\xi ,\alpha _{3})\cdot S=0$, $R(\xi ,\alpha _{3})\cdot P=0$, $R(\xi ,\alpha _{3})\cdot S=0$ and $P\cdot C=0$. Besides this, we classify $(k,\mu)$-paracontact manifolds. Also we researched conformally flat and $\phi $-conformally flat a $(k,\mu )-$paracontact metric manifolds.

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Cite This Article

Uygun, P., Atçeken, M. (2023). On $(k,\mu )$-Paracontact Manifold Satisfying Some Curvature Conditions. Turkish Journal of Mathematics and Computer Science, Volume: 15 Issue: 1. https://doi.org/10.47000/tjmcs.1153650

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