Harmonic maps into sub-Riemannian Lie groups

2023/05/10 by Erlend Grong, Grong, Erlend, Irina Markina +1
Mathematics · Physics and Astronomy · #53C17 #58E20 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2305.06096

openalex publication_date 2023/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define harmonic maps between sub-Riemannian manifolds by generalizing known definitions for Riemannian manifolds. We establish conditions for when a horizontal map into a Lie group with a left-invariant metric structure is a harmonic map. We show that sub-Riemannian harmonic maps can be abnormal or normal, just as sub-Riemannian geodesics. We illustrate our study by presenting the equations for harmonic maps into the Heisenberg group.

Related

• Back to harmonic mappings of compact Riemannian manifolds
• Biharmonic homomorphisms between Riemannian Lie groups
• Sub-semi-Riemannian geometry on H-type groups
• Sub-Riemannian geometry and Lie groups. Part I
• Eells-Sampson type theorems for subelliptic harmonic maps from sub-Riemannian manifolds