On Locally Conformal Kaehler Submersions

Year 2024, Volume: 17 Issue: 2, 507 - 518

Çağrıhan Çimen , Beran Pirinççi , Hakan Mete Taştan , Deniz Ulusoy

https://doi.org/10.36890/iejg.1461324

Abstract

We study locally conformal Kaehler submersions, i.e., almost Hermitian submersions whose total manifolds are locally conformal Kaehler. We prove that the vertical distribution of a locally conformal Kaehler submersion is totally geodesic iff the Lee vector field of total manifold is vertical. We also obtain the O'Neill tensors $\tilde{\mathcal{A}}$ and $\tilde{\mathcal{T}}$ with respect to the Weyl connection of a locally conformal Kaehler submersion. Then, we proved that the horizontal distribution of such a submersion is integrable iff $\tilde{\mathcal{A}} \equiv 0$. Finally, we get Chen-Ricci inequalities for locally conformal Kaehler space form submersions and Hopf space form submersions.

Keywords

Locally conformal Kaehler manifold, almost Hermitian submersion, Hopf space form submersion, O'Neill tensors, horizontal distribution

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