B.-Y. Chen's inequalities for Riemannian submersion and their applications
Differential Geometry
2026-05-20 v2
Abstract
In this paper, we introduce B.-Y. Chen inequalities for Riemannian submersions between Riemannian manifolds. We derive these inequalities for vertical, horizontal, and mixed distributions, establishing relationships between intrinsic invariants and extrinsic invariants. We also investigate the corresponding equality cases. As applications, the results are obtained for submersions whose total space is a real, complex, generalized Sasakian space form. Several examples are provided to illustrate both equality and strict inequality cases.
Keywords
Cite
@article{arxiv.2602.15301,
title = {B.-Y. Chen's inequalities for Riemannian submersion and their applications},
author = {Ravindra Singh and Mukut Mani Tripathi},
journal= {arXiv preprint arXiv:2602.15301},
year = {2026}
}