Uniwersytet Łódzki

Título: Bisectors and foliations in complex hyperbolic space

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Conferenciante: Maciej Czarnecki (Uniwersytet Łódzki, Polonia)

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Resumen: In the complex hyperbolic space $\mathbb{CH}^n$ there are no hypersurfaces (of real dimension $2n−1$) which are totally geodesic. The hypersurfaces imitating this condition as well as possible are bisectors i.e. equidistants from pair of points. Every bisector is uniquely described by their poles i.e. two distinct points on the ideal boundary. A spane (rep. complex spine) of the bisector is the geodesic (resp. complex geodesic) joining poles. In my talk I shall formulate a local condition for a family of bisector to form a foliation of $\mathbb{CH}^n$ and observe these foliations on the ideal boundary which has a structure of Heisenberg group. Moreover, we shall give examples of cospinal foliations and compare the situation with totally geodesic foliations of real hyperbolic space.

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Fecha: 15 de junio de 2018, 11:30 - 12:30
Lugar: Seminario 1, IEMath-GR

The course will be given by Prof. Maciej Czarnecki from Uniwersytet Łódzki

Content

1. Hyperbolic and conformal geometry
2. Introduction to the theory of foliations
3. Description of foliations with specific geometric properties which are defined conformally or through the second fundamental form
4. New results and applications of conformal geometry