Abstract
We give a complete classification of Levi-degenerate hypersurfaces of finite type in ℂ2 with two-dimensional symmetry groups. Our analysis is based on the classification of two-dimensional Lie algebras and an explicit description of isotropy groups for such hypersurfaces, which follows from the construction of Chern–Moser type normal forms at points of finite type, developed in [M. Kolář, Normal forms for hypersurfaces of finite type in ℂ2, Math. Res. Lett. 12 (2005), pp. 897–910].
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