Year: 2024
Type: article
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.
Institutions: Marmara University, Istanbul University, Istinye University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4402672329