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

 

Decomposability preserving curvature operators with an application to Einstein manifolds


Authors: Michael R. Gabel and Stanley M. Zoltek
Journal: Proc. Amer. Math. Soc. 90 (1984), 303-308
MSC: Primary 53C25; Secondary 53B20
MathSciNet review: 727255
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Abstract: In this paper we examine curvature operators that preserve decomposability. In particular, we prove that if at each point of an Einstein manifold $ M$ the sectional curvature operator is nonsingular and preserves decomposability, and the sectional curvature is either nonnegative or nonpositive, then $ M$ is a space of nonzero constant curvature.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0727255-9
PII: S 0002-9939(1984)0727255-9
Keywords: Curvature operator, decomposability preserving, Einstein manifold, constant curvature
Article copyright: © Copyright 1984 American Mathematical Society