The Fourth Fundamental Form <i>IV</i> 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 E4. We find the Gauss map of helicoidal hypersurface in E4. 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.

Keywords

• four dimension
• Dini-type helicoidal hypersurface
• Gauss map
• shape operator
• curvatures
• fourth fundamental form