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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Quadric representation of a submanifold
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by Ivko Dimitrić PDF
Proc. Amer. Math. Soc. 114 (1992), 201-210 Request permission

Abstract:

If $x: M^n \to E^m$ is an isometric immersion of a smooth manifold into a Euclidean space then the map $\tilde {x} = x x^{\mathrm {t}}$]> (t denotes transpose) is called the quadric representation of $M$. $\tilde {x}$ is said to be of finite type ($k$-type) if it can be decomposed into a sum of finitely many $(k)$ eigenfunctions of Laplacian from different eigenspaces. We study map $\tilde {x}$ in general, especially as related to the condition of being of finite type. Certain classification results are obtained for manifolds with $1$-and $2$-type quadric representation.
References
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Additional Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 114 (1992), 201-210
  • MSC: Primary 53C40; Secondary 53C42
  • DOI: https://doi.org/10.1090/S0002-9939-1992-1086324-1
  • MathSciNet review: 1086324