@article{Camarinha2024, 
author = {Margarida Camarinha},
title = {A natural 4th-order generalization of the geodesic problem},
year = {2024},
journal = {Electronic Research Archive},
volume = {32},
number = {5},
pages = {3396-3412},
keywords = {geodesics, Riemannian cubics, Euler-Lagrange equations, Euler-Poincaré equations},
url = {https://www.sciopen.com/article/10.3934/era.2024157},
doi = {10.3934/era.2024157},
abstract = {We propose a fourth-order extension of the geodesic problem arising in the continuity of the study of Riemannian cubics. We consider the variational problem in a Riemannian manifold and derive the Euler-Lagrange equation. For the special situation of Lie groups, we use Euler-Poincaré reduction to obtain the reduced equation on the Lie algebra.}
}