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

Ebenfelt, Peter; Duong Ngoc Son; Zaitsev, Dmitri

Math. Res. Lett. 25, No. 1, 75-84 (2018).

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.

Reviewer: Yunus E. Zeytuncu (Dearborn)

MSC:

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

Keywords:

strictly pseudoconvex domains; umbilical points

Citations:

Zbl 0302.32015