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

Speaker：Ling Yang (Fudan University)

Time：2026-5-17 10:30

Location：Conference Room S102 at Experiment Building at Haiyun Campus

Abstract:

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.