The first eigenvalue of the Dirac operator on compact Kähler manifolds
type: Item
instance of: scholarly article
title: The first eigenvalue of the Dirac operator on compact Kähler manifolds
zbMATH Open document ID: 0832.53054
DOI: 10.1007/BF02099477
author: Andrei Moroianu
published in: Communications in Mathematical Physics
publication date: 1995-08-22T00:00:00Z
review text: The first eigenvalue \(\lambda_1\) of the Dirac operator on a compact Kähler spin manifold of odd complex dimension \(m\) satisfies \(\lambda^2_1 \geq m^{-1} (m + 1){s\over 4}\). Here \(s\) is the lower bound of the scalar curvature. This estimate is due to \textit{K.-D. Kirchberg} [Ann. Global Anal. Geom. 4, 291-325 (1986; Zbl 0629.53058)]. The author describes the manifolds for which equality holds in this estimate. For \(m = 4l+ 1\) this is the complex projective space and for \(m = 4l + 3\) these are twistor spaces of quaternionic Kähler manifolds of positive scalar curvature.
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 58J50
zbMATH DE Number: 778992
zbMATH Keywords: first eigenvalue
zbMATH Keywords: Dirac operator
zbMATH Keywords: Kähler spin manifold
reviewed by: Hans-Bert Rademacher
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 778992