The Fourth Fundamental Form IV of Dini-Type Helicoidal Hypersurface in the Four Dimensional Euclidean Space

Abstract

We introduce the fourth fundamental form of a Dini-type helicoidal hypersurface in the four dimensional Euclidean space E-4. We find the Gauss map of helicoidal hypersurface in E-4. We obtain the characteristic polynomial of shape operator matrix. Then, we compute the fourth fundamental form matrix IV of the Dini-type helicoidal hypersurface. Moreover, we obtain the Dini-type rotational hypersurface, and reveal its differential geometric objects.