Decomposability preserving curvature operators with an application to Einstein manifolds

Gabel, Michael R.; Zoltek, Stanley M.

doi:10.1090/S0002-9939-1984-0727255-9

Decomposability preserving curvature operators with an application to Einstein manifolds
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by Michael R. Gabel and Stanley M. Zoltek PDF

Proc. Amer. Math. Soc. 90 (1984), 303-308 Request permission

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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