Decomposability preserving curvature operators with an application to Einstein manifolds
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- by Michael R. Gabel and Stanley M. Zoltek
- Proc. Amer. Math. Soc. 90 (1984), 303-308
- DOI: https://doi.org/10.1090/S0002-9939-1984-0727255-9
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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.References
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Bibliographic Information
- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 90 (1984), 303-308
- MSC: Primary 53C25; Secondary 53B20
- DOI: https://doi.org/10.1090/S0002-9939-1984-0727255-9
- MathSciNet review: 727255