The Principal Curvatures and the Third Fundamental Form of Dini-Type Helicoidal Hypersurface in 4-Space
Erhan G¨uler *
Bartın University, Faculty of Sciences, Department of Mathematics, 74100 Bartın, Turkey
*Author to whom correspondence should be addressed.
Abstract
We consider the principal curvatures and the third fundamental form of Dini-type helicoidal hypersurface D(u, v, w) in the four dimensional Euclidean space E4. We find the Gauss map e of helicoidal hypersurface in E4. We obtain characteristic polynomial of shape operator matrix S. Then, we compute principal curvatures ki=1;2;3, and the third fundamental form matrix III of D.
Keywords: Four dimensional, Dini-type helicoidal hypersurface, Gauss map, principal curvatures, the third fundamental form.