Rotational hypersurfaces of space forms with constant scalar curvature
We denote by \(N_ c\) the simply connected n-dimensional space form of constant curvature \(c=0,1\) or -1. Let M be a complete rotational hypersurface of \(N_ c\) with constant scalar curvature S. In this interesting, clearly written paper the author classifies these hypersurfaces in the cases \(c=0,-1\) and presents partial results for \(c=1\). Moreover he determines the admissible values of S in each of the three cases and gives a geometrical description of the hypersurfaces according to the values of S. In particular he proves that S is precisely greater than or equal to the space form curvature, except in the case \(c=1\) where any value greater than (n-3)/(n-1) is admissible. Surprising examples of embedded hypersurfaces in the case \(c=1\) with \(S<1\) are presented, which are not isometric to a product of spheres.
scientific article; zbMATH DE number 4138705
scientific article