Preprint 50/2006
σk-scalar curvature and eigenvalues of the Dirac operator
Guofang Wang
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Submission date: 17. May. 2006
Pages: 9
published in: Annals of global analysis and geometry, 30 (2006) 1, p. 65-71 
DOI number (of the published article): 10.1007/s10455-006-9022-z
Bibtex
MSC-Numbers: 53C21, 53C27
Keywords and phrases: $\sigma_k$ scalar curvature, dirac operator, eigenvalue
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Abstract:
On a 4-dimensional closed spin manifold 
,
the eigenvalues of the Dirac operator can be estimated from below
by the total 
-scalar curvature of 
as follows
Equality implies
that is a
round sphere
and the corresponding eigenspinors are Killing spinors.