Dursun, Uǧur Hypersurfaces with pointwise 1-type Gauss map. (English) Zbl 1136.53015 Taiwanese J. Math. 11, No. 5, 1407-1416 (2007). Summary: We prove that an oriented hypersurface \(M\) of a Euclidean space \(E^{n+1}\) has pointwise 1-type Gauss map of the first kind if and only if \(M\) has constant mean curvature. Then we conclude that all oriented isoparametric hypersurfaces of \(E^{n+1}\) have 1-type Gauss map. We also show that a rational hypersurface of revolution in a Euclidean space \(E^{n+1}\) has pointwise 1-type Gauss map of the second kind if and only if it is a right \(n\)-cone. Cited in 13 Documents MSC: 53B25 Local submanifolds Keywords:hypersurface of revolution; mean curvature; finite type; Gauss map PDFBibTeX XMLCite \textit{U. Dursun}, Taiwanese J. Math. 11, No. 5, 1407--1416 (2007; Zbl 1136.53015) Full Text: DOI