A sphericity criterion for strictly pseudoconvex hyper surfaces in ${\mathbb{C}}^2$ via invariant curves

Florian Bertrand, Giuseppe Della Sala, Bernhard Lamel

We prove that if every chain on a strictly pseudoconvex hypersurface $M$ in ${\mathbb{C}}^2$ coincides with the boundary of a stationary disc, then $M$ is locally spherical.