Surfaces in a pseudo-Euclidean space with planar normal sections (Q1124137)

In [J. Geom. 20, 122--127 (1983; Zbl 0518.53005)] the reviewer proved that if \(M\) is a surface in a Euclidean \(m\)-space \(E^m\) with planar normal sections and if locally \(M\) does not lie in a 3-dimensional subspace of \(E^m\), then \(M\) is an open subset of a Veronese surface in a 5-dimensional subspace of \(E^m\). In this article, the author studies the corresponding problems for pseudo-Riemannian surface \(M\) in a pseudo-Euclidean space. In particular, he obtains a complete classification of surfaces in a pseudo-Euclidean space with planar normal sections and parallel mean curvature vector.