Eigenvalue estimates for the Dirac operator on Kähler–Einstein manifolds of even complex dimension

In the case of a Kähler–Einstein manifold of positive scalar curvature and even complex dimension, an improved lower bound for the first eigenvalue of the Dirac operator is given. It is shown by a general construction that there are manifolds for which this new lower bound itself is the first eigenv...

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Bibliographic Details
Published inAnnals of global analysis and geometry Vol. 38; no. 3; pp. 273 - 284
Main Author Kirchberg, K.-D.
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.10.2010
Springer Nature B.V
Subjects
Analysis
Differential Geometry
Eigenvalues
Estimates
Geometry
Global Analysis and Analysis on Manifolds
Mathematical analysis
Mathematical Physics
Mathematics
Mathematics and Statistics
Original Paper
Studies
Topological manifolds
Lower bound
Kähler–Einstein manifold
58J50
Eigenvalue
53C27
Dirac operator
83C60
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Summary:In the case of a Kähler–Einstein manifold of positive scalar curvature and even complex dimension, an improved lower bound for the first eigenvalue of the Dirac operator is given. It is shown by a general construction that there are manifolds for which this new lower bound itself is the first eigenvalue.
ISSN:0232-704X
1572-9060
DOI:10.1007/s10455-010-9212-6