Killing Magnetic Curves in Sol Space

Erjavec, Zlatko; Inoguchi, Jun-ichi

doi:10.1007/s11040-018-9272-6

Cited by 20 publications

(9 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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“…and the (1, 1)-tensor ϕ given in base (e i ) i=1,3 by ϕ (e 1 ) = e 2 ; ϕ (e 2 ) = −e 1 and ϕ (e 3 ) = 0 (12) we have…”

Section: Preliminariesmentioning

confidence: 99%

“…Interesting results on Killing magnetic curves are given in Euclidian 3space ( [9]), Minkowski 3-space ( [8]), S 2 × R ( [17]), SL(2, R) ( [10]), Sol Space ( [12]), warped product manifold ( [15]), almost paracontact manifold ( [5]), Almost Cosymplectic Sol Space ( [11]) and in Walker manifolds ( [2]).…”

Section: Introductionmentioning

confidence: 99%

Explicit formulas for Killing magnetic curves in Heisenberg group

Derkaoui,

Hathout

2021

Preprint

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“…Recently, Killing vector fields have been used in study of magnetic curves. Killing magnetic curves in Euclidean space, Minkowski spacetime, Sol space, S 2 × R space and Walker manifolds were studied in [4,5], [7], [14] and [1], respectively.…”

Section: Killing Vector Fields In Sol Spacementioning

confidence: 99%