  We introduce the notion of K-correspondence, and show that many Calabi-Yau
varieties carry a lot of self-K-isocorrespondences, which furthermore satisfy
the property of multiplying the canonical volume form by a constant of modulus
different from 1. This leads to the introduction of a modified
Kobayashi-Eisenman pseudovolume form, for which we are able to prove many
instances of the Kobayashi conjecture.
