On Translation Curves and Geodesics in Sol^4_1 (CROSBI ID 324640)
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Erjavec, Zlatko ; Maretić, Marcel
engleski
On Translation Curves and Geodesics in Sol^4_1
A translation curve in a homogeneous space is a curve such that for a given unit vector at the origin, translation of this vector is tangent to the curve in its every point. Translation curves coincide with geodesics in most Thurston spaces, but not in twisted product Thurston spaces. Moreover, translation curves seem more intuitive and simpler than geodesics. In this paper, we determine translation curves in Sol^4_1 space. Their curvature properties are discussed and translation spheres are presented. Finally, characterization of geodesics in Sol^4_1 space is given.
translation curve ; geodesic ; solvable Lie group ; Sol^4_1 space
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