A family of compact strictly pseudoconvex hypersurfaces in $$\mathbb{C}^2$$ without umbilical points.(English)Zbl 1408.32033

The authors answer a well-known question of S. S. Chern and J. Moser [Acta Math. 133, 219–271 (1974; Zbl 0302.32015)], and provide explicit examples of smooth strictly pseudoconvex domains $$\Omega\subset\mathbb{C}^2$$ such that the boundary $$b\Omega$$ has no umbilical points.

MSC:

 32T15 Strongly pseudoconvex domains 30F45 Conformal metrics (hyperbolic, Poincaré, distance functions) 32V05 CR structures, CR operators, and generalizations

Zbl 0302.32015
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