Special homogeneous surfaces
Differential Geometry
2024-12-11 v1 High Energy Physics - Theory
Algebraic Geometry
Abstract
We classify hyperbolic polynomials in two real variables that admit a transitive action on some component of their hyperbolic level sets. Such surfaces are called special homogeneous surfaces, and they are equipped with a natural Riemannian metric obtained by restricting the negative Hessian of their defining polynomial. Independent of the degree of the polynomials, there exist a finite number of special homogeneous surfaces. They are either flat, or have constant negative curvature.
Cite
@article{arxiv.2303.18228,
title = {Special homogeneous surfaces},
author = {David Lindemann and Andrew Swann},
journal= {arXiv preprint arXiv:2303.18228},
year = {2024}
}
Comments
26 pages, 12 figures