Kähler流形谱几何

Spectral geometry of Kähler manifolds

本文从谱几何的历史出发,介绍谱几何的起源与波动方程、量子力学的联系,以及Riemann流形特别是Kähler流形的谱几何相关问题与中国学者的一些工作.最后两节介绍我们在复射影空间谱刚性以及常全纯截面曲率谱刻画方面的工作.

In this paper,we begin with a historical account of spectral geometry,which originated from wave equations and quantum mechanics.We will review the spectral geometry of Riemannian manifolds,especially Kähler manifolds,and the works of Chinese mathematicians.In the last two sections,we introduce our works on spectral rigidity of complex projective spaces and spectral characterization of Kähler manifolds with constant holomorphic sectional curvature.