engleski

Translation Surfaces with Constant Curvatures in 3-dimensional Lorentz-Minkowski Space

Translation surfaces are surfaces generated by two curves moving along each other. In 3-dimensional Lorentz-Minkowski space, which is the smooth manifold R 3 with flat Lorentzian pseudometric, such surfaces can be classified with respect to the causal character of their generating curves (spacelike, timelike or null (lightlike)). In this talk, we analyse translation surfaces with at least one null generating curve, which we refer to as null-translation surfaces. By considering generatrices as graphs of two functions with respect to the axis coordinate, we determine all null-translation surfaces of constant mean curvature and show that the only null-translation surfaces of constant Gaussian curvature are cylindrical surfaces. We also present alternative approach in analysing null-translation surfaces via Frenet frame, respectively null frame, of generatrices of the surface, that provides the explicit parametrization of null-translation surfaces with non-vanishing constant mean curvature.

Null-translation surfaces, Minkowski space

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