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# Bisectors and foliations in complex hyperbolic space

## Maciej Czarnecki Uniwersytet Łódzki

In the complex hyperbolic space $\mathbb {C}\mathbb{H}^n$ 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 $\mathbb{ C}\mathbb{H}^n$ 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.

Seminario 1ª Planta, IEMATH

# Boundaries in Non-positive Curvature IV

## Maciej Czarnecki Uniwersytet Łódzki

Manifolds and spaces of non-positive curvature
Ideal boundary
Contracting boundary
Applications to foliations and laminations.

Seminario, 1ª Planta, IEMath

# Boundaries in Non-positive Curvature III

## Maciej Czarnecki Uniwersytet Łódzki

Manifolds and spaces of non-positive curvature
Ideal boundary
Contracting boundary
Applications to foliations and laminations.

Seminario, 1ª Planta, IEMath

# Boundaries in Non-positive Curvature II

## Maciej Czarnecki Uniwersytet Łódzki

Manifolds and spaces of non-positive curvature
Ideal boundary
Contracting boundary
Applications to foliations and laminations.

Seminario, 1ª Planta, IEMath

# Boundaries in Non-positive Curvature I

## Maciej Czarnecki Uniwersytet Łódzki

Manifolds and spaces of non-positive curvature
Ideal boundary
Contracting boundary
Applications to foliations and laminations.

Seminario, 1ª Planta, IEMath

# Foliations with special geometric properties III

## Maciej Czarnecki Uniwersytet Łódzki

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

iEMath-Gr, Seminario 1ª planta

# Foliations with special geometric properties II

## Maciej Czarnecki Uniwersytet Łódzki

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

iEMath-Gr, Seminario 1ª planta

# Foliations with special geometric properties I

## Maciej Czarnecki Uniwersytet Łódzki

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

iEMath-Gr, Seminario 1ª planta

Number of talks
8
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