On Killing Magnetic Curves in Sl(2, ℝ) Geometry

Erjavec, Zlatko

doi:10.1016/s0034-4877(19)30096-5

Cited by 15 publications

(6 citation statements)

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“…The aim is a better understanding of the geometry of the underlying space. To conclude, we choose a few works from the huge list of papers studying this topic: [27,[30][31][32][33][34][35][36] (see also references therein). In this paper, we investigated magnetic geodesics in a 3-dimensional Lie group endowed with a left invariant almost cosymplectic structure that defined the magnetic field.…”

Section: Discussionmentioning

confidence: 99%

Magnetic Geodesic in (Almost) Cosymplectic Lie Groups of Dimension 3

Munteanu

2022

Mathematics

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In this paper, we study contact magnetic geodesics in a 3-dimensional Lie group G endowed with a left invariant almost cosymplectic structure. We distinguish the two cases: G is unimodular, and G is nonunimodular. We pay a careful attention to the special case where the structure is cosymplectic, and we write down explicit expressions of magnetic geodesics and corresponding magnetic Jacobi fields.

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Section: Discussionmentioning

confidence: 99%

Magnetic Geodesic in (Almost) Cosymplectic Lie Groups of Dimension 3

Munteanu

2022

Mathematics

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“…In [11] the author derived the equation of minimal surface and gave fundamental examples of minimal surfaces. In [12] Z. Erjavec discussed the so-called Killing magnetic curves. In [42] the authors discussed visualization methods of the considered geometry.…”

Section: Sl 2 R Geometrymentioning

confidence: 99%

Classical Notions and Problems in Thurston Geometries

Szirmai¹

2022

Preprint

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Of the Thurston geometries, those with constant curvature geometries (Euclidean E 3 , hyperbolic H 3 , spherical S 3 ) have been extensively studied, but the other five geometries, H 2 ×R, S 2 ×R, Nil, SL 2 R, Sol have been thoroughly studied only from a differential geometry and topological point of view. However, classical concepts highlighting the beauty and underlying structure of these -such as geodesic curves and spheres, the lattices, the geodesic triangles and their surfaces, their interior sum of angles and similar statements to those known in constant curvature geometries can be formulated. These have not been the focus of attention. In this survey, we summarize our results on this topic and pose additional open questions.

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“…In [15], the same authors studied these curves in three-dimensional Minkowski space. In [5], Erjavec gave some characterizations about Killing magnetic curves in SL(2, R). In [6] and [7], Killing magnetic curves were investigated in Sol space and almost cosymplectic Sol space, respectively.…”

Section: Introductionmentioning

confidence: 99%