Clairaut and Einstein conditions for locally conformal Kaehler submersions

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Pirinççi B., Çimen Ç., Ulusoy D.

Istanbul Journal of Mathematics, vol.1, no.1, pp.28-39, 2023 (Peer-Reviewed Journal)

• Publication Type: Article / Article
• Volume: 1 Issue: 1
• Publication Date: 2023
• Doi Number: 10.26650/ijmath.2023.00003
• Journal Name: Istanbul Journal of Mathematics
• Page Numbers: pp.28-39
• Istanbul University Affiliated: Yes

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.