Subvarieties of quotients of bounded symmetric domains uniruled by holomorphic geodesic curves

Abstract

For uniruled projective manifolds it has been demonstrated that the study of tautological foliations arising from minimal rational curves is crucial for the understanding of the geometry of such manifolds. In the special case of Hermitian symmetric manifolds M of the compact type it is natural to consider an analogous dual situation, viz., tautological foliations arising from minimal disks on finite-volume quotients X :=Omega/Gamma of bounded symmetric domains Omega Subset Bbb C^n subset M. Here by a minimal disk on X we mean the image of a minimal disk on Omega under the uniformization map pi: Omega o X.