Isometric immersions of Lorentz space with parallel second fundamental forms (Q799953)

The paper is concerned with isometric immersions into pseudo-Euclidean spaces \({\mathbb{R}}^ m_ i\) of signature (i,m-i), which possess parallel second fundamental form. The main result is the classification of these immersions of the following type \({\mathbb{R}}^ n_ 0\to {\mathbb{R}}_ 1^{n+k}\), \({\mathbb{R}}_ 1^ n\to {\mathbb{R}}_ 1^{n+2}\), and \({\mathbb{R}}^ n_ 1\to {\mathbb{R}}_ 2^{n+2}\). For that the construction of special examples is needed. Besides the complete umbilic submanifolds of \({\mathbb{R}}^ m_ i\) are classified.