Holomorphic contact via Pascal map and operator theory

Abstract

We give an intrinsic definition of point-wise contact between holomorphic Hermitian vector bundles by introducing a canonical bundle map, called the Pascal map, on their jet bundles. Combined with a holomorphic gluing condition, point-wise contact is further extended to contact along an analytic hyper-surface and we characterize it by the curvatures and their covariant derivatives on the vector bundles. The Pascal map has a realization in operator theory where our study applies to unitary equivalence of shift operators on function spaces.