Loop space of a K\"ahler manifold
Differential Geometry
2025-01-28 v1 Complex Variables
Abstract
We prove that the loop space of a K\"ahler manifold inherits a K\"ahler structure. Then we prove that equipped with this natural metric the loop space is complete and unbounded. Additionally, we show that a geodesic on the loop space can be constructed by piecing together geodesics from each individual leaf.
Keywords
Cite
@article{arxiv.2501.15984,
title = {Loop space of a K\"ahler manifold},
author = {M. Anakkar},
journal= {arXiv preprint arXiv:2501.15984},
year = {2025}
}
Comments
10 pages