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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Factorization of curvature operators


Author: Jaak Vilms
Journal: Trans. Amer. Math. Soc. 260 (1980), 595-605
MSC: Primary 53C20; Secondary 15A63, 53B25, 53C40
DOI: https://doi.org/10.1090/S0002-9947-1980-0574802-7
MathSciNet review: 574802
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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 {\,^2}V$ into itself. Necessary and sufficient conditions are given for R to admit factorization as $ R\, = \,\Lambda {\,^2}L$, 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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DOI: https://doi.org/10.1090/S0002-9947-1980-0574802-7
Article copyright: © Copyright 1980 American Mathematical Society