In this paper a generalization of helices in the three-dimensional Galilean and the pseudo-Galilean space is proposed. The equiform general helices, which represent a generalization of "ordinary" helices, are defined and characterized. Particularly, all obtained results can be transferred to other Cayley-Klein spaces, including Euclidean.

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Abstract. In this paper some geometric properties of SL(2, R) geometry are considered, the minimal surface equation is derived and fundamental examples of minimal surfaces are given. IntroductionThe SL(2, R) geometry is one of eight homogeneous Thurston 3-geometriesThe Riemannian manifold (M, g) is called homogeneous if for any x, y ∈ M there exists an isometry Φ : M → M such that y = Φ(x). The two-and three-dimensional homogeneous geometries are discussed in detail in [16]. In 1997 Emil Molnár proposed (see [9]) a projective spherical model of homogeneous geometries as a unified geometrical model. He believed that this model could be a starting point for possible attack on the Thurston conjecture. He also introduced the hyperboloid model of SL(2, R) geometry and determined the corresponding metric tensor. The hyperboloid model of SL(2, R) geometry is described in details in [3,11,12] where geodesics, the fibre translation group and translation curves (with corresponding spheres) are given. Generally, SL(2, R) geometry, because of its specificity, represents a rich area for future investigation. Recently, there are several papers that discuss ball packing and regular prism tilings in SL(2, R) geometry (see [13,14,17]).2010 Mathematics Subject Classification. 53A40.

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