The rigidity of minimal Legendrian submanifolds in the Euclidean spheres via eigenvalues of fundamental matrices

报告人：杨翎（复旦大学）

时  间：2026年5月17日10:30

地  点：海韵园实验楼S102

内容摘要:

We study the rigidity problem for compact minimal Legendrian submanifolds in the unit Euclidean spheres via eigenvalues of fundamental matrices, which measure the squared norms of the second fundamental form restricted on all normal directions. By using Lu's inequality on the upper bound of the squared norm of Lie brackets of symmetric matrices, we establish a pinching theorem for such submanifolds, giving a new characterization for Calabi tori. This pinching condition can also be described by the eigenvalues of the Ricci curvature tensor, which is optimal for all dimensions. Meanwhile, when the third large eigenvalue of the fundamental matrix vanishes everywhere, we get an optimal rigidity theorem under a weaker pinching condition.

个人简介：

杨翎，复旦大学数学科学学院教授，博士生导师，国家优秀青年科学基金获得者。主要研究方向为微分几何。和国内外专家合作，在极小子流形、调和映照、平均曲率流等领域进行了深入研究，共撰写论文23篇，均发表在SCI杂志上,其中包括J. Diff. Geom., J. Math. Pures Appl., Adv. Math., Tran. Amer. Math., Calc. Var. PDE, Math. Z., Ann. Sc. Norm. Super. Pisa等权威期刊。

联系人：桂耀挺