4 papers
math.DG2026
Rigidity Results for Compact Submanifolds with Pinched Ricci Curvature in Euclidean and Spherical Space Forms
Jianquan Ge, Ya Tao, Yi Zhou
For compact submanifolds in Euclidean and Spherical space forms with Ricci curvature bounded below by a function of mean curvature, we prove that the submanifold is e…
math.DG2026
Normal Scalar Curvature Inequality on a Class of Austere Submanifolds
Jianquan Ge, Ya Tao, Yi Zhou
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. W…
math.DG2025
Austere Matrices, Austere Submanifolds and Dupin Hypersurfaces
Jianquan Ge, Yi Zhou
Motivated by Bryant's research on austere subspaces and Cartan's isoparametric hypersurfaces with 3 distinct principal curvatures, we construct three families of austere submanifol…
math.DG2024
Recent Progress on Austere Submanifolds
Jianquan Ge, Yi Zhou
This is a brief survey of recent results related to austere submanifolds, mainly based on the papers [24,25].