We introduce the fourth fundamental form of the torus hypersurface in the four dimensional Euclidean space. We also compute I, II, III and IV fundamental forms of a torus hypersurface.

We study curvature formulas and the fourth fundamental form IV of hypersurfaces in the four dimensional Euclidean geometry E4. We calculate fourth fundamental form and curvatures for hypersurfaces, and also for hypersphere. ...

We study the fourth fundamental form of the factorable hypersurface in the four dimensional Euclidean space E4. We obtain I, II, III, and IV fundamental forms of a factorable hypersurface.

Numerical approximation of minimal surface is an important problem in form-finding of structural membranes. In this paper, we present a novel approach to construct minimal surface from a given boundary by quasi-harmonic ...

We study and examine the rotational hypersurface and its Gauss map in Euclidean four-space E4 . We calculate the Gauss map, the mean curvature and the Gaussian curvature of the rotational hypersurface and obtain some ...

We give the classical isometric minimal helicoidal and rotational surfaces using generalized Bour’s theorem in Euclidean 3-space. Furthermore, we investigate the minimality and have same Gauss map of the surfaces.

We consider Ulisse Dini-type helicoidal hypersurfaces with timelike axis in Minkowski 4-space E41 . Calculating the Gaussian and the mean curvatures of the hypersurfaces, we demonstrate some special symmetries for the ...