A normal form for a special class of curvature operators

Zoltek, Stanley M.

doi:10.1090/S0002-9939-1980-0572314-3

A normal form for a special class of curvature operators
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by Stanley M. Zoltek

Proc. Amer. Math. Soc. 79 (1980), 614-618

DOI: https://doi.org/10.1090/S0002-9939-1980-0572314-3

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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 ${\Lambda ^4}$.

References

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I. M. Singer and J. A. Thorpe, The curvature of $4$-dimensional Einstein spaces, Global Analysis (Papers in Honor of K. Kodaira), Univ. Tokyo Press, Tokyo, 1969, pp. 355–365. MR 0256303
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Stanley M. Zoltek, Nonnegative curvature operators: some nontrivial examples, J. Differential Geometry 14 (1979), no. 2, 303–315. MR 587555