Quadratic representation of a submanifold in pseudo-Euclidean space
Let \(x\) be an isometric immersion of a pseudo-Riemannian manifold \(M\) in a pseudo-Euclidean space \(E\). The map \(\widetilde x=xx^t\) \((t\) denotes transpose) is called the quadric representation of \(M\). The authors study the map \(\widetilde x\) subject to one of the following conditions: (a) \(\widetilde x\) is of finite type; (b) \(\Delta\widetilde x=B\widetilde x+C\), where \(\Delta\) is the Laplacian operator and \(B\) and \(C\) are two constant matrices.NEWLINENEWLINEFor the entire collection see [Zbl 0954.00038].
scientific article; zbMATH DE number 1641150