Clairaut and Einstein conditions for locally conformal Kaehler submersions

Year 2023, Volume: 1 Issue: 1, 28 - 39, 21.06.2023

Beran Pirinççi , Çağrıhan Çimen , Deniz Ulusoy

https://doi.org/10.26650/ijmath.2023.00003

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.

Keywords

Riemannian submersion, almost Hermitian submersion, locally conformal Kaehler submersion, Clairaut submersion, Einstein manifold

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