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.

In this paper, we give explicit parametrizations for Bour type surfaces in various three-dimensional space forms, using Weierstrass-type representations. We also determine classes and degrees of some Bour type zero mean ...

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 consider rotational hypersurface in the four-dimensional Euclidean space E4. We study the Gauss map G of rotational hypersurface in E4 with respect to the so-called Cheng–Yau operator L1 acting on the functions defined ...

We study curvatures C_i (i=1,2,3) of translation hypersurface in the four dimensional Euclidean space. We also give some relations on C_i of translation hypersurface.

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 ...