@article{Grong2023, 
author = {Erlend Grong and Irina Markina},
title = {Harmonic maps into sub-Riemannian Lie groups},
year = {2023},
journal = {Communications in Analysis and Mechanics},
volume = {15},
number = {3},
pages = {515-532},
keywords = {Sub-Riemannian manifolds, horizontal maps, harmonic maps, Darboux derivative},
url = {https://www.sciopen.com/article/10.3934/cam.2023025},
doi = {10.3934/cam.2023025},
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.}
}