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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A holonomy proof of the positive curvature operator theorem


Author: W. A. Poor
Journal: Proc. Amer. Math. Soc. 79 (1980), 454-456
MSC: Primary 53C20
MathSciNet review: 567991
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Abstract: Extending work of Bochner-Yano and M. Berger, D. Meyer proved that if the curvature operator of a compact, oriented, Riemannian manifold M has positive eigenvalues, then M is a rational homology sphere. Here a proof is given using Chern's holonomy formula for the Laplacian on M; for completeness, a quick proof of Chern's formula is included.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1980-0567991-7
PII: S 0002-9939(1980)0567991-7
Keywords: Eigenvalue of curvature operator, Laplacian, rational homology sphere, holonomy algebra
Article copyright: © Copyright 1980 American Mathematical Society