Espaço de módulos de triplas de geodésicas complexas no espaço hiperbólico complexo de dimensão 4

Abstract

The principal purpose of this work is to describe the moduli space of ordered triples of complex geodesics in complex hyperbolic space of dimension 4 relative to the action of the group of holomorphic isometries PU(4,1). Also, we describe the moduli space of ordered triples of geodesics (non-oriented) in real hyperbolic space of dimension 3 and 4. The main innovations of this work are the use of the polar sets of geodesics (real and complex) and the notion of the transition angles of the triples of geodesics in question.