Minimal geodesics on GL(n) for left-invariant, right-O(n)-invariant Riemannian metrics

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...

Homogeneous Geodesics of Left Invariant Randers Metrics on a Three-Dimensional Lie Group

In this paper we study homogeneous geodesics in a three-dimensional connected Lie group G equipped with a left invariant Randers metric and investigates the set of all homogeneous geodesics. We show that there is a three-dimensional unimodular Lie group with a left invariant non-Berwaldian Randers metric which admits exactly one homogeneous geodesic through the identity element. Mathematics Sub...

Left-Invariant Riemannian Elasticity: a distance on shape diffeomorphisms ?

In inter-subject registration, one often lacks a good model of the transformation variability to choose the optimal regularization. Some works attempt to model the variability in a statistical way, but the re-introduction in a registration algorithm is not easy. In [1], we interpreted the elastic energy as the distance of the Green-St Venant strain tensor to the identity. By changing the Euclid...

A remark on left invariant metrics on compact Lie groups

The investigation of manifolds with non-negative sectional curvature is one of the classical fields of study in global Riemannian geometry. While there are few known obstruction for a closed manifold to admit metrics of non-negative sectional curvature, there are relatively few known examples and general construction methods of such manifolds (see [Z] for a detailed survey). In this context, it...

Topologically Left Invariant Mean on Dual Semigroup Algebras