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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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

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