Homogeneous Geodesics in 3-dimensional Homogeneous Affine Manifolds

Abstrakt

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.

Klíčová slova

• Geodesics
• 3-dimensional manifold
• Homogeneous space