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Helicoidal surfaces in Minkowski space with constant mean curvature and constant Gauss curvature

Rafael López; Esma Demir — 2014

Open Mathematics

We classify all helicoidal non-degenerate surfaces in Minkowski space with constant mean curvature whose generating curve is a the graph of a polynomial or a Lorentzian circle. In the first case, we prove that the degree of the polynomial is 0 or 1 and that the surface is ruled. If the generating curve is a Lorentzian circle, we prove that the only possibility is that the axis is spacelike and the center of the circle lies on the axis.

Timelike $B_{2}$ -slant helices in Minkowski space $E_{1}^{4}$

Ahmad T. Ali; Rafael López — 2010

Archivum Mathematicum

We consider a unit speed timelike curve $α$ in Minkowski 4-space $𝐄_{1}^{4}$ and denote the Frenet frame of $α$ by ${𝐓, 𝐍, 𝐁_{1}, 𝐁_{2}}$ . We say that $α$ is a generalized helix if one of the unit vector fields of the Frenet frame has constant scalar product with a fixed direction $U$ of $𝐄_{1}^{4}$ . In this work we study those helices where the function $〈 𝐁_{2}, U 〉$ is constant and we give different characterizations of such curves.

Constant mean curvature surfaces bounded by a circle.

López, Rafael — 2006

Divulgaciones Matemáticas

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Helicoidal surfaces in Minkowski space with constant mean curvature and constant Gauss curvature

Timelike B 2 -slant helices in Minkowski space E 1 4

Constant mean curvature surfaces bounded by a circle.

Timelike $B_{2}$ -slant helices in Minkowski space $E_{1}^{4}$