English

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}
}