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Factorization of Curvature Operators

Jaak Vilms
Transactions of the American Mathematical Society
Vol. 260, No. 2 (Aug., 1980), pp. 595-605
DOI: 10.2307/1998025
Stable URL: http://www.jstor.org/stable/1998025
Page Count: 11
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Factorization of Curvature Operators
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Abstract

Let $V$ be a real finite-dimensional vector space with inner product and let $R$ be a curvature operator, i.e., a symmetric linear map of the bivector space $\Lambda^2V$ into itself. Necessary and sufficient conditions are given for $R$ to admit factorization as $R = \Lambda^2L$, with $L$ a symmetric linear map of $V$ into itself. This yields a new characterization of Riemannian manifolds that admit local isometric embedding as hypersurfaces of Euclidean space.

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