Ricci pinched compact submanifolds in space forms
Differential Geometry
2023-11-06 v2
Abstract
We investigate the compact submanifolds in Riemannian space forms of nonnegative sectional curvature that satisfy a lower bound on the Ricci curvature, that bound depending solely on the length of the mean curvature vector of the immersion. While generalizing the results, we give a positive answer to a conjecture by H. Xu and J. Gu in (2013, Geom. Funct. Anal. 23). Our main accomplishment is the elimination of the need for the mean curvature vector field to be parallel.
Cite
@article{arxiv.2310.19021,
title = {Ricci pinched compact submanifolds in space forms},
author = {Marcos Dajczer and Theodoros Vlachos},
journal= {arXiv preprint arXiv:2310.19021},
year = {2023}
}