arXiv subjects

Marcelo Lopes Ferro

Publications and source records attributed to Marcelo Lopes Ferro.

3 recordsLinked to original sources

arXiv2025

Surfaces and Hypersurfaces with Prescribed Radial Mean Curvature

In this work, we provide a local classification of certain special classes of surfaces determined by the prescription of the radial mean curvature in terms of the height and angle functions. Moreover, we introduce a special class of hypersurfaces, and we also provide a local classification of these three-dimensional hypersurfaces whose second mean curvature vanishes. Finally, we present a recursive method for constructing such hypersurfaces, extending the same curvature prescription approach to higher dimensions.

math.DG↗

arXiv2021

New Flat surfaces in $S^3$

n this paper, we consider a method of constructing flat surfaces based on Ribaucour transformations in the sphere 3-space. By applying the theory to the flat torus, we obtain a families of complete flat surfaces in $S^3$ which are determined by several parameters. we provide explicit examples.

math.GT↗

arXiv2020

New Isothermic surfaces

In this paper, we consider a method of constructing isothermic surfaces based on Ribaucour transformations. By applying the theory to the cylinder, we obtain a three-parameter family of complete isothermic surfaces that contains n-bubble surfaces inside and outside of the cylinder. In addition, we also obtain one-parameter family of complete isothermic surface with planar ends. Such family of isothermic surfaces do not have constant mean curvature. As aplication we obtain explicit solutions of the Calapso equation.

math.GT↗