The rigidity of eigenvalues on Kähler manifolds with positive Ricci lower bound

2024/01/29 by Jianchun Chu, Feng Wang, Chu, Jianchun +3 · 3 citations
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2401.15830

Abstract

In this work, optimal rigidity results for eigenvalues on Kähler manifolds with positive Ricci lower bound are established. More precisely, for those Kähler manifolds whose first eigenvalue agrees with the Ricci lower bound, we show that the complex projective space is the only one with the largest multiplicity of the first eigenvalue. Moreover, there is a specific gap between the largest and the second largest multiplicity. In the Kähler--Einstein case, almost rigidity results for eigenvalues are also obtained.

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• On diameter rigidity for Kähler manifolds with positive holomorphic sectional curvature
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• Quantitative Obata's theorem in discrete setting

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