Geodesics and curvature of semidirect product groups

2001/03/23 by Cornelia Vizman, Vizman, Cornelia · 2 citations
Mathematics · Physics and Astronomy · #58B20 #58D05 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Nonlinear Waves and Solitons #math.DG #msc:58B20 #msc:58D05

paper · pdf · doi:10.48550/arxiv.math/0103141

10 pages, Latex2e

arxiv created 2001/03/23 · openalex publication_date 2001/03/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• 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

Related

• Half plane geometries
• Numerically modelling semidirect product geodesics
• Geodesics and Visual boundary of Horospherical Products
• A metric interpretation of the geodesic curvature in the Heisenberg group
• Vertically invariant minimal surfaces in unimodular semidirect products