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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Factorization of curvature operators
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by Jaak Vilms PDF
Trans. Amer. Math. Soc. 260 (1980), 595-605 Request permission


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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Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 260 (1980), 595-605
  • MSC: Primary 53C20; Secondary 15A63, 53B25, 53C40
  • DOI:
  • MathSciNet review: 574802