The Sturm spirals which can be introduced as those plane curves whose curvature radius is equal to the distance from the origin are embedded in to one parameter family of curves. In this paper, we consider the spacelike and timelike Sturmian spirals in Lorentz-Minkowski plane.

Canal surface is a surface formed as the envelope of a family of spheres whose centers lie on a space curve. In Minkowski 3-space, many authors studied canal surfaces. However, when one investigates the papers, it is obvious that the parametrizations of the canal surfaces were found with respect to only pseudo sphere S 2 1 (r). In this paper, we reconsider the canal surfaces for all Lorentz spheres which are pseudo sphere S 2 1 (r), pseudo-hyperbolic sphere H 2 (r) or lightlike cone C and we find the parametrizations of the surfaces. Moreover, we found the parametrization of the tubular surfaces with respect to all Lorentz spheres. Also, we study Weingarten and linear Weingarten type spacelike tubular surface obtained from pseudo-hyperbolic sphere H 2 0 (r) and the singular points of the spacelike tubular surface obtained from pseudo-hyperbolic sphere H 2 0 (r). Mathematics Subject Classification. 53B30, 53C50, 53A35.

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In this paper we consider some elastic spacelike and timelike curves in the Lorentz-Minkowski plane and obtain the respective vectorial equations of their position vectors in explicit analytical form. We study in more details the generalized Sturmian spirals in the Lorentz-Minkowski plane which simultaneously are elastics in this space.

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