Complex hyperbolic space

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In mathematics, more precisely in differential geometry, complex hyperbolic space is the symmetric space associated with the Lie group ${\displaystyle \mathrm {SU} (n,1)}$. It can be explicitely constructed by giving a metric on the unit ball in ${\displaystyle \mathbb {C} ^{n}}$. It is characterised by being the only simply connected Hermitian manifold whose holomorphic sectional curvature which is constant equal to -1.

See also[]

• Hyperbolic space

References[]

• Goldman, William M. (1999). Complex hyperbolic geometry. Oxford: Clarendon Press. p. xx + 316. ISBN 0-19-853793-X.

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