Universidad de Murcia

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math.DG2026★ 1 cited

A property that characterizes the Enneper surface and helix surfaces

Pascual Lucas, JosÃ© Antonio Ortega-YagÃ¼es

The main goal of this paper is to show that helix surfaces and the Enneper surface are the only surfaces in the 3-dimensional Euclidean space $R^{3}$ whose isogonal lines are general…

math.DG2026★ 3 cited

Concircular helices and concircular surfaces in Euclidean 3-space R3

Pascual Lucas, JosÃ© Antonio Ortega-YagÃ¼es

In this paper we characterize concircular helices in $R^{3}$ by means of a differential equation involving their curvature and torsion. We find a full description of concircular surf…

math.DG2026

L1-2-type surfaces in 3-dimensional De Sitter and anti De Sitter spaces

S. Carolina GarcÃa-MartÃnez, Pascual Lucas, H. FabiÃ¡n RamÃrez-Ospina

Let $M$ be an orientable surface immersed in the De Sitter space $S_{1}^{3}$ in $R_{1}^{4}$ or anti de Sitter space $H_{1}^{3}$ in $R_{2}^{4}$ . In the case that $M$ is of $L_{1}$ -2-type we prove tha…

math.DG2026★ 3 cited

Concircular hypersurfaces and concircular helices in space forms

In this paper, we find a full description of concircular hypersurfaces in space forms as a special family of ruled hypersurfaces. We also characterize concircular helices in 3-dime…