Quadric representation of a submanifold
| Autor: | Ivko Dimitrić |
|---|---|
| Rok vydání: | 1992 |
| Předmět: | |
| Zdroj: | Proceedings of the American Mathematical Society. 114:201-210 |
| ISSN: | 1088-6826 0002-9939 |
| DOI: | 10.1090/s0002-9939-1992-1086324-1 |
| Popis: | If x : M n → E m x: M^n \to E^m is an isometric immersion of a smooth manifold into a Euclidean space then the map x ~ = x x t \tilde {x} = x x^{\mathrm {t}} ]> (t denotes transpose) is called the quadric representation of M M . x ~ \tilde {x} is said to be of finite type ( k k -type) if it can be decomposed into a sum of finitely many ( k ) (k) eigenfunctions of Laplacian from different eigenspaces. We study map x ~ \tilde {x} in general, especially as related to the condition of being of finite type. Certain classification results are obtained for manifolds with 1 1 -and 2 2 -type quadric representation. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|