The affine approach to homogeneous geodesics in homogeneous Finsler spaces

Homogeneous geodesics in homogeneous Finsler spaces

In this paper, we study homogeneous geodesics in homogeneous Finsler spaces. We first give a simple criterion that characterizes geodesic vectors. We show that the geodesics on a Lie group, relative to a bi-invariant Finsler metric, are the cosets of the one-parameter subgroups. The existence of infinitely many homogeneous geodesics on compact semi-simple Lie group is established. We introduce ...

Homogeneous geodesics of left invariant Finsler metrics

In this paper, we study the set of homogeneous geodesics of a leftinvariant Finsler metric on Lie groups. We first give a simple criterion that characterizes geodesic vectors. As an application, we study some geometric properties of bi-invariant Finsler metrics on Lie groups. In particular a necessary and sufficient condition that left-invariant Randers metrics are of Berwald type is given. Fin...

Affine Embeddings of Homogeneous Spaces

Let G be a reductive algebraic group and H a closed subgroup of G. An affine embedding of the homogeneous space G/H is an affine G-variety with an open G-orbit isomorphic to G/H . The homogeneous space G/H admits an affine embedding if and only if G/H is a quasi-affine algebraic variety. We start with some basic properties of affine embeddings and consider the cases, where the theory is well-de...

Zero - Entropy Affine Maps on Homogeneous Spaces

Computation of the Cartan Spaces of Affine Homogeneous Spaces

Let G be a reductive algebraic group and H its reductive subgroup. Fix a Borel subgroup B ⊂ G and a maximal torus T ⊂ B. The Cartan space aG,G/H is, by definition, the subspace of Lie(T )∗ generated by the weights of B-semiinvariant rational functions on G/H . We compute the spaces aG,G/H.