We consider the Gauss map of the rotational hypersurface in the four dimensional Euclidean space. We define the mean curvature and the Gaussian curvature formulas. We also find some geometric ...

The surface theory has been working by many mathematicians, and also geometers for hundreds of years. We meet nice papers and books for the theory in the literature. In this paper, we consider deltohelicoidal surface in ...

We define a new kind of helicoidal surface of value m. A rotational surface which is isometric to the helicoidal surface of value m is revealed. In addition, we calculate some differential geometric properties of the ...

In this paper some relations are established between the Laplace-Beltrami operator and the curvatures of helicoidal surfaces in 3-Euclidean space. In addition, Bour’s theorem on the Gauss map, andsome special examples are given.

We define Ulisse Dini-type helicoidal hypersurfaces with spacelikeaxis in Minkowski 4-spaceE41. We compute the Gaussian and the mean curva-ture of the hypersurface. Moreover, we obtain some special symmetries to thecurvatures ...

In this study, we show that a Generalized helicoid with null axis is isometric to a rotation surface with null axis so that helices on the Helicoid correspond to parallel circles on the rotation surface in three dimensional ...

Geometers have been working the curve theory and the surface theory for hundreds of years. We see good works for the theories in the literature. In this work, we introduce cardiohelicoidal surface in the three dimensional ...

We considerUlisse Dini-type helicoidal hypersurface in Euclidean 4-space E4.We give some basic notions of the fourdimensional Euclidean geometry in section 2.In section 3, we consider Ulisse Dini helicoidal hypersurface.We ...

We consider an astrohelicoidal hypersurface which its profile curve has astroid curve in the four dimensional Euclidean space E4. We also calculate Gaussian curvature and the mean curvature, and Weingarten relation of the ...