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Goldman's and Mostow's works on bisectors in ℂ H n   provide the motivation for this paper. By a linear submanifold of ℂ H n   we mean a submanifold of the form exp( V ), where  V  is a subspace of  T x  ℂ H n   for some  x ∈ℂ H n  . In this case,  x  is called an origin of  L . Every bisector in ℂ H n   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.

Linear submanifolds and bisectors in ℂ H n