Holomorphic vector bundles on Kähler manifolds and totally geodesic foliations on Euclidean open domains

Monica Alice Aprodu; Marian Aprodu

doi:10.1016/j.difgeo.2015.01.002

paper

Holomorphic vector bundles on Kähler manifolds and totally geodesic foliations on Euclidean open domains

arXiv:1409.3701 · doi:10.1016/j.difgeo.2015.01.002

Abstract

In this Note we establish a relation between sections in globally generated holomorphic vector bundles on Kähler manifolds, isotropic with respect to a non-degenerate quadratic form, and totally geodesic foliations on Euclidean open domains. We find a geometric condition for a totally geodesic foliation to originate in a holomorphic vector bundle. For codimension-two foliations, this description recovers of P. Baird and J. C. Wood. The universal objects that play a key role are the orthogonal Grassmannians.