Publication at Faculty of Mathematics and Physics |
2009
Abstract
For studying homogeneous geodesics in Riemannian and pseudo- Riemannian geometry (on reductive homogeneous spaces) there is a simple algebraic formula. In the affine differential geometry, there is not such an universal formula.
In the present paper, we propose a simple method of investigation of affine homogeneous geodesics. As an application, we prove, among others, the existence of homogeneous geodesics for all homogeneous affine manifolds in dimension 2.