Title: Riemannian hypersubmersions from complex space forms

Authors: Kiran Meena, Bayram Sahin

Corresponding Author: Kiran Meena

Journal Name: Differential Geometry and its Applications

Publisher: Elsevier

Link/DOI: https://doi.org/10.1016/j.difgeo.2026.102421

Volume: 104

Year: 2026

Abstract: In this paper, we introduce the notions of vertical and horizontal hypersubmersions with non-trivial examples, which are Riemannian submersions from complex space forms onto Riemannian manifolds such that the fibers and the horizontal spaces are the tangent bundles of real hypersurfaces of the source space, respectively. This research problem opens a new direction in the theory of Riemannian submersions and is essentially a dual analog of the concept of real hypersurfaces in complex space forms. First, treating the fibers of a Riemannian submersion as hypersurfaces, we determine the geometric properties of the fibers and the tensor field T. In this case, the Hopf hypersurface is also taken into account, and the notion of Hopf vertical hypersubmersion is introduced. Under this notion, we examine complex space forms, including complex projective spaces and complex hyperbolic spaces, in terms of their principal curvatures. Furthermore, the case in which the horizontal distribution of Riemannian submersions of co-dimension 1 is considered. In this case, we investigate the character of the tensor field A and the horizontal space, and examine the sectional curvatures of planes in the source and target spaces.