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Proceedings of the American Mathematical Society

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



Quadric representation of a submanifold

Author: Ivko Dimitrić
Journal: Proc. Amer. Math. Soc. 114 (1992), 201-210
MSC: Primary 53C40; Secondary 53C42
MathSciNet review: 1086324
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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^{\text{t}}}$]> (<![CDATA[ $ {\text{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 $ \left( k \right)$ 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.

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Article copyright: © Copyright 1992 American Mathematical Society

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