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Journals / Istanbul Journal of Mathematics / 2026 / Volume: 1 Issue: 1

Clairaut and Einstein conditions for locally conformal Kaehler submersions

Beran Pirinççi(ISTANBUL UNIVERSITY)0000-0002-4692-9590
Çağrıhan Çimen(ISTANBUL UNIVERSITY)0009-0000-6331-9615
Deniz Ulusoy(ISTANBUL UNIVERSITY)0000-0002-0742-4047
Pages
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Publication Date
2023-06-21
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AI Summary & Key Takeaways

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

Finally, we obtain some formulas for sectional and holomorphic sectional curvatures for a locally conformal Kaehler submersion.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In the present paper, we study Clairaut submersions and Einstein conditions whose total manifolds are locally conformal Kaehler manifolds.
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Key Findings & Data:We first give a necessary and sufficient condition for a curve to be geodesic on total manifold of a locally conformal Kaehler submersion.
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Conclusion & Impact:Finally, we obtain some formulas for sectional and holomorphic sectional curvatures for a locally conformal Kaehler submersion.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Riemannian submersion · almost Hermitian submersion · locally conformal Kaehler submersion

Abstract

In the present paper, we study Clairaut submersions and Einstein conditions whose total manifolds are locally conformal Kaehler manifolds. We first give a necessary and sufficient condition for a curve to be geodesic on total manifold of a locally conformal Kaehler submersion. Then, we investigate conditions for a locally conformal Kaehler submersion to be a Clairaut submersion.We find the Ricci and scalar curvature formulas between any fiber of the total manifold and the base manifold of a locally conformal Kaehler submersion and give necessary and sufficient conditions for the total manifold of a locally conformal Kaehler submersion to be Einstein. Finally, we obtain some formulas for sectional and holomorphic sectional curvatures for a locally conformal Kaehler submersion.

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Cite This Article

Pirinççi, B., Çimen, Ç., Ulusoy, D. (2023). Clairaut and Einstein conditions for locally conformal Kaehler submersions. Istanbul Journal of Mathematics, Volume: 1 Issue: 1. https://doi.org/10.26650/ijmath.2023.00003

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