Abstract
We introduce the epitrochoidal hypersurfaces in four dimensional Euclidean space E^4. We serve notations of a Euclidean geometry E^4. Giving a definition of the rotational hypersurface, we define the epitrochoidal hypersurface, and calculate its differential geometric objects, such as the Gauss map and the curvatures. In the end, we reveal some relations for the curvatures of that type hypersurfaces.
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