Normal Scalar Curvature Inequality on a Class of Austere Submanifolds
Differential Geometry
2026-01-06 v2
Abstract
In this paper, we establish new normal scalar curvature inequalities on a class of austere submanifolds by proving sharper DDVV-type inequalities on associated austere subspaces. We also provide some examples of austere submanifolds in this class and point out one of them achieves the equality in our normal scalar curvature inequality everywhere. As a byproduct, we obtain a Simons-type gap theorem for closed austere submanifolds in unit spheres which belong to that class.
Keywords
Cite
@article{arxiv.2410.17761,
title = {Normal Scalar Curvature Inequality on a Class of Austere Submanifolds},
author = {Jianquan Ge and Ya Tao and Yi Zhou},
journal= {arXiv preprint arXiv:2410.17761},
year = {2026}
}
Comments
24 pages, any comments are welcome, accepted by Math. Z