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Proceedings of the American Mathematical Society

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



A normal form for a special class of curvature operators

Author: Stanley M. Zoltek
Journal: Proc. Amer. Math. Soc. 79 (1980), 614-618
MSC: Primary 53B20; Secondary 15A75
MathSciNet review: 572314
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Abstract: In the case of a 4-dimensional oriented inner product space Singer and Thorpe found a canonical form for a curvature operator which commutes with a generator of $ {\Lambda ^4}$, and used it to prove that the curvature function is completely determined by its critical point behavior. In dimension 5 we extend these results to curvature operators which commute with an element of $ {\Lambda ^4}$.

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Keywords: Curvature operator, normal form, critical point behavior, Einstein manifold, Bianchi identity, Grassmann quadratic 2-relations
Article copyright: © Copyright 1980 American Mathematical Society

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