We review part of the classical theory of curves and surfaces in 3-dimensional Lorentz-Minkowski space. We focus in spacelike surfaces with constant mean curvature pointing the differences and similarities with the Euclidean space.

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Abstract. We consider a curve α = α(s) in Minkowski 3-space E 3 1 and denote by {T, N, B} the Frenet frame of α. We say that α is a slant helix if there exists a fixed direction U of E 3 1 such that the function ⟨N(s), U ⟩ is constant. In this work we give characterizations of slant helices in terms of the curvature and torsion of α. Finally, we discuss the tangent and binormal indicatrices of slant curves, proving that they are helices in E 3 1 .

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In homogenous space Sol we study compact surfaces with constant mean curvature and with non-empty boundary. We ask how the geometry of the boundary curve imposes restrictions over all possible configurations that the surface can adopt. We obtain a flux formula and we establish results that assert that, under some restrictions, the symmetry of the boundary is inherited into the surface. MSC: 53A10