The Global Solutions to Cartan's Realization Problem
Differential Geometry
2022-12-02 v3
Abstract
We introduce a systematic method to solve a type of Cartan's realization problem. Our method builds upon a new theory of Lie algebroids and Lie groupoids with structure group and connection. This approach allows to find local as well as complete solutions, their symmetries, and to determine the moduli spaces of local and complete solutions. We apply our method to the problem of classification of extremal K\"ahler metrics on surfaces.
Cite
@article{arxiv.1907.13614,
title = {The Global Solutions to Cartan's Realization Problem},
author = {Rui Loja Fernandes and Ivan Struchiner},
journal= {arXiv preprint arXiv:1907.13614},
year = {2022}
}
Comments
Typos corrected. Several comments added and a correction to an example in Section 9.2. This is the final version accepted for publication in Memoirs of the AMS