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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].
math.DG2024
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 ei…
math.DG2024
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.DG2024
A survey on the DDVV-type inequalities
Jianquan Ge, Fagui Li, Zizhou Tang +1
In this paper, we give a survey on the history and recent developments on the DDVV-type inequalities.