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notes on complex hyperbolic geometry john r parker department of mathematical sciences university of durham durham dh1 3le england j r parker durham ac uk july 11 2003 contents 1 ...
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...Notes on complex hyperbolic geometry john r parker department of mathematical sciences university durham dh le england j ac uk july contents introduction space hermitian forms c three models cayley transforms isometries the unitary groups rst form second pu and its action classication boundary relation to heisenberg group horospherical coordinates cygan metric subspaces geodesics lines totally real lagrangian planes geodesic boundaries revisited distance formulae cross ratios between a point pairs theunit ball in has natural constant negative holomorphic sectional curva ture which we normalise be called bergman as such it model for h analogous n hr main dierence is that curvature no longer but pinched another standard paraboloid siegel domain this half just unit disc with poincar e hc generalisation plane dierent from more familiar higher dimensional an alternative description given by projective here take signature projectivising set gives taking suitable making choice section can rec...