Harmonic maps into sub-Riemannian Lie groups

被引：0

作者：

Grong, Erlend ^{[1
]}

Markina, Irina ^{[1
]}

机构：

[1] Univ Bergen, Dept Math, POB 7803, N-5020 Bergen, Norway

来源：

COMMUNICATIONS IN ANALYSIS AND MECHANICS | 2023年 / 15卷 / 03期

关键词：

Sub-Riemannian manifolds; horizontal maps; harmonic maps; Darboux derivative; REGULARITY;

D O I：

10.3934/cam.2023025

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：515 / 532

页数：18

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