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.
Original language | English |
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Journal | Mathematical Proceedings of the Cambridge Philosophical Society |
Volume | 177 |
Issue | 2 |
Pages (from-to) | 333-362 |
ISSN | 0305-0041 |
DOIs | |
Publication status | Published - 2024 |