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Rotational hypersurfaces of space forms with constant scalar curvature. (English) Zbl 0695.53040
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.
Reviewer: T.Hasanis

##### MSC:
 53C40 Global submanifolds
Full Text:
##### References:
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