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.
All Science Journal Classification (ASJC) codes
- Applied Mathematics