Annali di Matematica Pura ed Applicata

, Volume 154, Issue 1, pp 385–402

Pseudodistances and Pseudometrics on real and complex manifolds


  • Sergio Venturini
    • Scuola Normale Superiore

DOI: 10.1007/BF01790358

Cite this article as:
Venturini, S. Annali di Matematica pura ed applicata (1989) 154: 385. doi:10.1007/BF01790358


In this paper we study the relationships between a class of distances and infinitesimal metrics on real and complex manifolds and their behavior under differentiable and holomorphic mappings. Some application to Riemannian and Finsler geometry are given and also new proofs and generalizations of some results of Royden, Harris and Reiffen on Kobayashi and Carathéodory metrics on complex manifolds are obtained. In particular we prove that on every complex manifold (finite or infinite- dimensional) the Kobayashi distance is the integrated form of the corresponding infinitesimal metric.

Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1989