High Quality Content by WIKIPEDIA articles! In mathematics, the Caratheodory metric is a metric defined on the open unit ball of a complex Banach space that has many similar properties to the Poincare metric of hyperbolic geometry. It is named after the Greek mathematician Constantin Caratheodory.There is an associated notion of Caratheodory length for tangent vectors to the ball B. Let x be a point of B and let v be a tangent vector to B at x; since B is the open unit ball in the vector space X, the tangent space TxB can be identified with X in a natural way, and v can be thought of as an element of X.

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