Quaternions, Monge-Amp\`ere structures and $k$-surfaces
Differential Geometry
2022-10-07 v1
Abstract
In [15] Labourie develops a theory of immersed surfaces of prescribed extrinsic curvature which has since found widespread applications in hyperbolic geometry, general relativity, Teichm\"uller theory, and so on. In this chapter, we present a quaternionic reformulation of these ideas. This yields simpler proofs of the main results whilst pointing towards the higher-dimensional generalisation studied by the author in [25].
Cite
@article{arxiv.2210.02664,
title = {Quaternions, Monge-Amp\`ere structures and $k$-surfaces},
author = {Graham Smith},
journal= {arXiv preprint arXiv:2210.02664},
year = {2022}
}
Comments
Requested chapter for forthcoming book. Some new results and simpler proofs of existing results