Homogeneous Geodesics in 3-dimensional Homogeneous Affine Manifolds

Zdeněk Dušek; Oldřich Kowalski; Zdeněk Vlášek

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2011)

  • Volume: 50, Issue: 1, page 29-42
  • ISSN: 0231-9721

Abstract

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For studying homogeneous geodesics in Riemannian and pseudo-Riemannian geometry (on reductive homogeneous spaces) there is a simple algebraic formula which works, at least potentially, in every given case. In the affine differential geometry, there is not such a universal formula. In the previous work, we proposed a simple method of investigation of homogeneous geodesics in homogeneous affine manifolds in dimension 2. In the present paper, we use this method on certain classes of homogeneous connections on the examples of 3-dimensional Lie groups.

How to cite

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Dušek, Zdeněk, Kowalski, Oldřich, and Vlášek, Zdeněk. "Homogeneous Geodesics in 3-dimensional Homogeneous Affine Manifolds." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 50.1 (2011): 29-42. <http://eudml.org/doc/196677>.

@article{Dušek2011,
abstract = {For studying homogeneous geodesics in Riemannian and pseudo-Riemannian geometry (on reductive homogeneous spaces) there is a simple algebraic formula which works, at least potentially, in every given case. In the affine differential geometry, there is not such a universal formula. In the previous work, we proposed a simple method of investigation of homogeneous geodesics in homogeneous affine manifolds in dimension 2. In the present paper, we use this method on certain classes of homogeneous connections on the examples of 3-dimensional Lie groups.},
author = {Dušek, Zdeněk, Kowalski, Oldřich, Vlášek, Zdeněk},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {affine connection; affine Killing vector field; homogeneous manifold; homogeneous geodesic; affine connection; affine Killing vector field; homogeneous manifold; homogeneous geodesic},
language = {eng},
number = {1},
pages = {29-42},
publisher = {Palacký University Olomouc},
title = {Homogeneous Geodesics in 3-dimensional Homogeneous Affine Manifolds},
url = {http://eudml.org/doc/196677},
volume = {50},
year = {2011},
}

TY - JOUR
AU - Dušek, Zdeněk
AU - Kowalski, Oldřich
AU - Vlášek, Zdeněk
TI - Homogeneous Geodesics in 3-dimensional Homogeneous Affine Manifolds
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2011
PB - Palacký University Olomouc
VL - 50
IS - 1
SP - 29
EP - 42
AB - For studying homogeneous geodesics in Riemannian and pseudo-Riemannian geometry (on reductive homogeneous spaces) there is a simple algebraic formula which works, at least potentially, in every given case. In the affine differential geometry, there is not such a universal formula. In the previous work, we proposed a simple method of investigation of homogeneous geodesics in homogeneous affine manifolds in dimension 2. In the present paper, we use this method on certain classes of homogeneous connections on the examples of 3-dimensional Lie groups.
LA - eng
KW - affine connection; affine Killing vector field; homogeneous manifold; homogeneous geodesic; affine connection; affine Killing vector field; homogeneous manifold; homogeneous geodesic
UR - http://eudml.org/doc/196677
ER -

References

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