A characterization theorem gives a holomorphic extension criterion for when a smooth strictly pseudoconvex CR hypersurface admits real-analytic coordinates.
Invariants and Umbilical Points on Three Dimensional CR Manifolds embedded in $\mathbb C^2$
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abstract
We introduce a new sequence of CR invariant determinants on a three dimensional CR manifold $M$ embedded in $\mathbb C^2$. The lowest order invariant $\det A_3$ represents E. Cartan's 6th order invariant (the umbilical "tensor"), whose zero locus yields the set of umbilical points on $M$. As an application of this new presentation of the umbilical invariant, we show that generic, almost circular perturbations of the unit sphere always contain curves or surfaces of umbilical points.
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2019 1verdicts
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Real-analytic coordinates for smooth strictly pseudoconvex CR-structures
A characterization theorem gives a holomorphic extension criterion for when a smooth strictly pseudoconvex CR hypersurface admits real-analytic coordinates.