Special homogeneous curves - Lindemann, David (MATHEMATICA SCANDINAVICA, 2024)
We classify all special homogeneous curves. A special homogeneous curve $\mathcal {H}$ consists of connected components of the hyperbolic points in the level set $\{h=1\}$ of a homogeneous polynomial $h$ in two real variables of degree at least three, and admits a transitive group action of a subgroup $G\subset GL(2)$ on $\mathcal {H}$ that acts via linear coordinate change.