Some graph type hypersurfaces in a semi-Euclidean space (Q2703134)

First the authors observe that: (i) a lightlike surface of revolution in \({\mathbb{R}}^3_1\) with timelike axis must be the lightcone, (ii) there is no lightlike surface of revolution with spacelike axis in \({\mathbb{R}}^3_1\). NEWLINENEWLINENEWLINENext they consider a graph type hypersurface in a semi-Euclidean space \({\mathbb{R}}^{n+1}_q\) given by \(x^{n+1}=x^1+\ldots +x^k+ F(x^{k+1}+\ldots +x^n)\), where \(F\) is a smooth function. The authors give conditions for such a hypersurface to be lightlike or minimal.