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.

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

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

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

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

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

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

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