Linear submanifolds and bisectors in ℂHn
-
Po-Hsun Hsieh
Abstract
Goldman's and Mostow's works on bisectors in ℂHn provide the motivation for this paper. By a linear submanifold of ℂHn we mean a submanifold of the form exp(V), where V is a subspace of TxℂHn for some x∈ℂHn. In this case, x is called an origin of L. Every bisector in ℂHn is a linear submanifold. We obtain some results about linear submanifolds, bisectors, and their intersections, and generalize some results about bisectors to linear submanifolds. Among other things, we characterize minimal linear submanifolds, obtain sufficient conditions for two linear submanifolds to intersect in a nice set and for a geodesic to lie in a linear submanifold, and obtain equivalent conditions for two bisectors to intersect at constant angle.
© Walter de Gruyter
Articles in the same Issue
- Boundary value problem with an oblique derivative for uniformly elliptic operators with discontinuous coefficients
- Radon transforms on the symmetric group and harmonic analysis of a class of invariant Laplacians
- Linear submanifolds and bisectors in ℂHn
- Affine Hughes groups acting on 4-dimensional compact projective planes
- A parallelism for contact conformal sub-Riemannian geometry
- Finite groups with smooth one fixed point actions on spheres
Articles in the same Issue
- Boundary value problem with an oblique derivative for uniformly elliptic operators with discontinuous coefficients
- Radon transforms on the symmetric group and harmonic analysis of a class of invariant Laplacians
- Linear submanifolds and bisectors in ℂHn
- Affine Hughes groups acting on 4-dimensional compact projective planes
- A parallelism for contact conformal sub-Riemannian geometry
- Finite groups with smooth one fixed point actions on spheres
