DECOMPOSITION OF COMPLEX HYPERBOLIC ISOMETRIES BY TWO COMPLEX SYMMETRIES

摘要

Let PU(2, 1) denote the holomorphic isometry group of the 2-dimensional complex hyperbolic space H-C(2), and the group SU(2, 1) is a 3-fold covering of PU(2, 1): PU(2, 1) = SU(2, 1)/{omega I : omega(3) = 1}. We study how to decompose a given pair of isometries (A, B). SU(2, 1) 2 under the form A = I1I2 and B = I3I2, where the I-k's are complex symmetries about complex lines. If (A, B) can be written as above, we call it is C-decomposable. The main results are decomposability criteria, which improve and supplement the result of [17].