On Translation Curves and Geodesics in Sol 1 4

Zlatko Erjavec () and Marcel Maretić
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Zlatko Erjavec: Faculty of Organization and Informatics, University of Zagreb, HR-42000 Varaždin, Croatia
Marcel Maretić: Faculty of Organization and Informatics, University of Zagreb, HR-42000 Varaždin, Croatia

Mathematics, 2023, vol. 11, issue 8, 1-10

Abstract: 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 often seem more intuitive and simpler than geodesics. In this paper, we determine translation curves in Sol 1 4 space. Their curvature properties are discussed and translation spheres are presented. Finally, characterization of geodesics in Sol 1 4 space is given.

Keywords: translation curve; geodesic; solvable Lie group; Sol 1 4 space (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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