Kobayashi metric

In mathematics, the original Kobayashi metric is a pseudometric (or pseudodistance) on complex manifolds introduced by Kobayashi (1967). It can be viewed as the dual of the Carathéodory metric, and has been extended to complex analytic spaces and almost complex manifolds. On Teichmüller space the Kobayashi metric coincides with the Teichmüller metric; on the unit ball, it coincides with the Bergman metric.