Holomorphic Projective Structures and Invariant Distances

Abstract

In analogy with the intrinsic pseudo-distance on complex analytic spaces (see [3]), I introduced a projectively invariant pseudo-distance on affine and projective manifolds, [4], The same construction can be applied to holomorphic affine and, more generally, projective structures to produce an intrinsic pseudo-distance which depends not only on the complex structure but on the given holomorphic projective structure. In this lecture, I will discuss a few examples of holomorphic projective structures and their projective pseudo-distances, referring for details to [7].