Quadric representation of a submanifold

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Abstract

If x : Mn⟶ Em is an isometric immersion of a smooth manifold into a Euclidean space then the map x = xxt (t denotes transpose) is called the quadric representation of M . x is said to be of finite type (fc-type) if it can be decomposed into a sum of finitely many (k) eigenfunctions of Laplacian from different eigenspaces. We study map 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.

Original languageEnglish (US)
Pages (from-to)201-210
Number of pages10
JournalProceedings of the American Mathematical Society
Volume114
Issue number1
DOIs
StatePublished - Jan 1992

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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