We study two parameters families of Bour-type and Enneper-type minimal surfaces using the Weierstrass representation in the four dimensional Euclidean space. We obtain implicit algebraic equations, degree and classes of ...

The Cornu spirals on plane are the curves whose curvatures are linear. Generalized planar cornu spirals and Euler spirals in E3, the curves whose curvatures are linear are deÖned in [1,5]. In this study, these curves are ...

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 study on a new kind of surface covered by translation and factorable (TF-type) surfaces in the three dimensional Euclidean space. We calculate I and III Laplace-Beltrami operator surfaces of a TF-type ...

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 ...