On Magnetic Curves in Almost Cosymplectic Sol Space

Erjavec, Zlatko; Inoguchi, Jun-ichi

doi:10.1007/s00025-020-01235-y

Cited by 15 publications

(10 citation statements)

References 17 publications

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“…In [16] the authors determined magnetic curves corresponding to the Killing magnetic fields in Sol. In [14] Z. Erjavec and J. Inoguchi discussed magnetic curves with respect to the almost cosymplectic structure and investigated the curvature properties of these curves.…”

Section: Related Results In Sol 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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Section: Related Results In Sol Geometrymentioning

confidence: 99%

Classical Notions and Problems in Thurston Geometries

Szirmai¹

2022

Preprint

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“…The study in [19] is an interesting survey on slant curves in 3-dimensional almost contact metric geometry where the slant curves in 3-dimensional solvable Lie groups equipped with natural left invariant almost contact metric structure are studied as well. Slant magnetic curves in almost cosymplectic space Sol 3 are studied in [20]. Lie group Sol 3 may be realized as the unimodular Lie group with λ 2 = −λ 1 = 0 (see, for example, §3 in [21]).…”

Section: Unimodular Casementioning

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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“…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. In [9], Munteanu and Nistor classified Killing magnetic curves in S 2 × R. In [3], Calvaruso, Munteanu and Perrone obtained a complete classification for the Killing magnetic curves in three-dimensional almost paracontact manifolds.…”

Section: Introductionmentioning

confidence: 99%