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Zero CR-curvature equations for Levi degenerate hypersurfaces via Pocchiola's invariants
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abstract
In our earlier articles we studied tube hypersurfaces in ${\mathbb C}^3$ that are 2-nondegenerate and uniformly Levi degenerate of rank 1. In particular, we showed that the vanishing of the CR-curvature of such a hypersurface is equivalent to the Monge equation with respect to one of the variables. In the present paper we provide an alternative shorter derivation of this equation by utilizing two invariants discovered by S. Pocchiola. We also investigate Pocchiola's invariants in the rigid case and give a partial classification of rigid 2-nondegenerate uniformly Levi degenerate of rank 1 hypersurfaces with vanishing CR-curvature.
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On Differential Invariants of Parabolic Surfaces
For generic parabolic surfaces in R^3 modulo the special affine group, the algebra of differential invariants is generated through invariant differentiation by the fourth-order invariant W and one new fifth-order invariant M.
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