The first eigenvalue of the Dirac operator on locally reducible Riemannian manifolds

2005/02/25 by Bogdan Alexandrov, Alexandrov, Bogdan
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Spectral Theory in Mathematical Physics #math.DG #msc:35P15 #msc:53C15 #msc:53C27

paper · pdf · doi:10.48550/arxiv.math/0502536

7 pages

arxiv created 2005/02/25 · arxiv updated 2009/12/01

Abstract

We prove a lower estimate for the first eigenvalue of the Dirac operator on a compact locally reducible Riemannian spin manifold with positive scalar curvature. We determine also the universal covers of the manifolds on which the smallest possible eigenvalue is attained.

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