New examples of complete hypersurfaces with constant positive scalar curvature in the Euclidean space
For complete 2-dimensional surfaces \(M\) in the 3-dimensional Euclidean space \(E^3\) with constant Gaussian curvature, it is well known that \(M\) is a sphere, a plane or a cylinder. For complete \(n\)-dimensional hypersurfaces (\(n\geq 3\)) with constant scalar curvature, the known examples are flat hypersurfaces, spheres, generalized cylinders, some rotational hypersurfaces and some complete hypersurfaces with constant non positive scalar curvature. In this paper, the author constructs a new family of noncompact complete hypersurfaces in \(E^{n+1}\) with constant positive scalar curvature by the method of equivariant differential geometry.
scientific article; zbMATH DE number 5835138
scientific article