Factorization of curvature operators
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- by Jaak Vilms
- Trans. Amer. Math. Soc. 260 (1980), 595-605
- DOI: https://doi.org/10.1090/S0002-9947-1980-0574802-7
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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.References
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Bibliographic Information
- © Copyright 1980 American Mathematical Society
- 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