Kähler manifolds with small eigenvalues of the Dirac operator and a conjecture of Lichnerowicz
type: Item
instance of: scholarly article
title: Kähler manifolds with small eigenvalues of the Dirac operator and a conjecture of Lichnerowicz
zbMATH Open document ID: 0946.53040
author: Andrei Moroianu
publication date: 1999-11-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/75396
review text: Using the well-known Lichnerowicz formula for the square of the Dirac operator, Th. Friedrich proved a first inequality for the eigenvalues of the Dirac operator on a compact Riemannian spin manifold. He obtained a lower bound which contains the scalar curvature of the underlying manifold. The limiting case of this inequality is characterized by the existence of real Killing spinors. In 1986 K.-D. Kirchberg improves this inequality for Kähler manifolds. Kähler manifolds of odd complex dimension satisfying the limiting case were classified by the author in 1994. In 1997, the author gave several partial results for the even-dimensional case, especially properties of the Ricci tensor of such a manifold. The paper under review gives a complete description for all compact spin Kähler manifolds of even complex dimension and positive scalar curvature with least possible first eigenvalue of the Dirac operator.
reviewed by: Katharina Habermann
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 58C40
Mathematics Subject Classification ID: 53C27
zbMATH DE Number: 1355994
zbMATH Keywords: spin Kähler manifold
zbMATH Keywords: Kirchberg's inequality
zbMATH Keywords: Dirac operator
MaRDI profile type: Publication
Wikidata QID: Q122961561
OpenAlex ID: W4320823089
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DOI: 10.5802/AIF.1732
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published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 1355994