Pseudodistances and pseudometrics on real and complex manifolds (Q914902)

The author studies the relationships between a class of Kobayashi-type and Carathéodory pseudo-distances and a class of infinitesimal Finsler metrics on real and complex manifolds and their behavior under differentiable and holomorphic mappings. Applications to Riemannian and Finsler geometries as well as proofs of generalizations of classical results are also given. In particular, a proof that on every complex manifold (finite or infinite-dimensional), the Kobayashi distance is the integrated form of the corresponding infinitesimal metric is exhibited.