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 ...

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.

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 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 ...

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 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 ...

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 ...

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 ...