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arXiv · 2303.18228

Special homogeneous surfaces

David Lindemann·Andrew Swann
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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.

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David Lindemann, Andrew Swann. 2023-03-31. Special homogeneous surfaces. https://doi.org/10.1017/s0305004124000252

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