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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 51 Issue: 2

Some results on paracontact metric $(k,\mu)$-manifolds with respect to the Schouten-van Kampen connection

Selcen Yüksel Perktaş(ADIYAMAN UNIVERSITY)0000-0002-8848-0621
U.c. De(University of Calcutta)0000-0002-2116-7382
Ahmet Yıldız(INONU UNIVERSITY)0000-0002-9799-1781
Pages
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Publication Date
2022-04-01
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AI Summary & Key Takeaways

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

Finally, we present some results related to almost Yamabe solitons in a paracontact metric $(k,\mu )$-manifold equipped with the Schouten-van Kampen connection and construct an example which verifies some of our results.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In the present paper we study certain symmetry conditions and some types of solitons on paracontact metric $(k,\mu )$-manifolds with respect to the Schouten-van Kampen connection.
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Key Findings & Data:We investigate paracontact metric $(k,\mu )$-manifolds satisfying $\breve{Q}\cdot \breve{R}_{cur}=0$\ with respect to the Schouten-van Kampen connection.
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Conclusion & Impact:Finally, we present some results related to almost Yamabe solitons in a paracontact metric $(k,\mu )$-manifold equipped with the Schouten-van Kampen connection and construct an example which verifies some of our results.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Schouten-van Kampen connection · Ricci semisymmetric · Einstein manifold

Abstract

In the present paper we study certain symmetry conditions and some types of solitons on paracontact metric $(k,\mu )$-manifolds with respect to the Schouten-van Kampen connection. We prove that a Ricci semisymmetric paracontact metric $(k,\mu )$-manifold with respect to the Schouten-van Kampen connection is an $\eta $-Einstein manifold. We investigate paracontact metric $(k,\mu )$-manifolds satisfying $\breve{Q}\cdot \breve{R}_{cur}=0$\ with respect to the Schouten-van Kampen connection. Also, we show that there does not exist an almost Ricci soliton in a $(2n+1)$-dimensional paracontact metric $(k,\mu )$-manifold with respect to the Schouten-van Kampen connection such that $k>-1$ or $k<-1$. In case of the metric is being an almost gradient Ricci soliton with respect to the Schouten-van Kampen connection, then we state that the manifold is either $N(k)$-paracontact metric manifold or an Einstein manifold. Finally, we present some results related to almost Yamabe solitons in a paracontact metric $(k,\mu )$-manifold equipped with the Schouten-van Kampen connection and construct an example which verifies some of our results.

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Cite This Article

Perktaş, S. Y., De, U., Yıldız, A. (2022). Some results on paracontact metric $(k,\mu)$-manifolds with respect to the Schouten-van Kampen connection. Hacettepe Journal of Mathematics and Statistics, Volume: 51 Issue: 2. https://doi.org/10.15672/hujms.941744

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