On ideal hypersurfaces of Euclidean 4-space (Q375163)

In 1990, B. Y. Chen introduced the notion of ideal immersion. In the present paper, the author classifies all ideal hypersurfaces with two distinct principle curvatures in the Euclidean 4-space and proves that such ideal hypersurfaces are always rigid. In the end, the author constructs an example of a minimal ideal hypersurface with three principal curvatures in \(E^4\) which are not necessary rigid. The results are interesting.