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.

OriginalsprogEngelsk
TidsskriftMathematical Proceedings of the Cambridge Philosophical Society
Vol/bind177
Nummer2
Sider (fra-til)333-362
ISSN0305-0041
DOI
StatusUdgivet - 2024

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