Abstract
In this paper 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 $E^{n+1}$ has 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.
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