A natural 4th-order generalization of the geodesic problem
Margarida Camarinha · Electronic Research Archive · 2024
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.