Geodesics and curvature of semidirect product groups

Abstract

Geodesics and curvature of semidirect product groups with right invariant metrics are determined. In the special case of an isometric semidirect product, the curvature is shown to be the sum of the curvature of the two groups. A series of examples, like the magnetic extension of a group, are then considered.

arXiv comment10 pages, Latex2e

References in corpus (1)

• The Camassa-Holm equation as a geodesic flow on the diffeomorphism group

Cited by in corpus (4)

• Geodesic Equations on Diffeomorphism Groups
• Differential-geometrical approach to the dynamics of dissipationless incompressible Hall magnetohydrodynamics I: Lagrangian mechanics on semidirect product of two volume preserving diffeomorphisms and conservation laws
• Differential-geometrical approach to the dynamics of dissipationless incompressible Hall magnetohydrodynamics: II. Geodesic formulation and Riemannian curvature analysis of hydrodynamic and magnetohydrodynamic stabilities
• The geometry of barotropic flow