Invariant Connections, Lie Algebra Actions, and Foundations of Numerical Integration on Manifolds
Hans Z. Munthe-Kaas, Ari Stern, Olivier Verdier
SIAM Journal on Applied Algebra and Geometry2020
Abstract
This paper establishes fundamental connections between Lie algebra actions, invariant connections, and numerical integration on manifolds. We develop a comprehensive framework showing how geometric structures on homogeneous spaces determine the structure of numerical integrators that preserve these structures. The results provide theoretical foundations for Lie group methods in numerical analysis.
Cite this publication
@article{hanszmunthekaas2020invariant,
author = {Hans Z. Munthe-Kaas and Ari Stern and Olivier Verdier},
title = {Invariant Connections, Lie Algebra Actions, and Foundations of Numerical Integration on Manifolds},
journal = {SIAM Journal on Applied Algebra and Geometry},
year = {2020},
doi = {10.1137/19M1252879},
eprint = {1903.10056},
archivePrefix = {arXiv}
}