Lower bounds for the eigenvalue of the transversal Dirac operator on a Kähler foliation
type: Item
instance of: scholarly article
title: Lower bounds for the eigenvalue of the transversal Dirac operator on a Kähler foliation
zbMATH Open document ID: 1027.53051
DOI: 10.1016/S0393-0440(02)00122-5
author: Seoung Dal Jung
author: Tae Ho Kang
published in: Journal of Geometry and Physics
publication date: 2003-03-23T00:00:00Z
review text: The authors consider a foliated Riemann manifold with a Kähler spin foliation and give a lower bound for the square of the eigenvalues of the transversal Dirac operator (which, if the foliation is a point foliation, simply reduces to the Dirac operator on a Kähler manifold). In the case the lower bound is attained and its square root is itself an eigenvalue of the transversal Dirac operator, the Kähler foliation is minimal, transversally Einsteinian of odd complex dimension with nonnegative constant transversal scalar curvature.
Mathematics Subject Classification ID: 53C27
Mathematics Subject Classification ID: 53C12
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 58J50
zbMATH DE Number: 1886811
zbMATH Keywords: Kähler foliation
zbMATH Keywords: foliated Riemann manifold
zbMATH Keywords: Dirac operator
zbMATH Keywords: transversal Dirac operator
zbMATH Keywords: transversal Killing spinor
zbMATH Keywords: transversally Einsteinian
zbMATH Keywords: transversal scalar curvature
reviewed by: Eugen Pascu
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1886811