Pseudoholomorphic Bundles over Almost Hermitian 6-Manifolds
by
Robert L. Bryant
Duke University, USA

Plenary Lecture

A pseudo-holomorphic bundle over an almost complex manifold M is a complex vector bunddle E --> M endowed with a connection whose curvature is of type (1, 1). When the complex dimension of M is at least 3, the generic almost complex structure admits no non-trivial pseudoholomorphic bundles.

In this talk, I will discuss the geometry of an interesting class of almost complex 6-manifolds that have the property that they have many pseudo-holomorphic bundles, roughly speaking, almost as many as integrable complex structures do. I call this class of almost complex structures `quasi-integrable'. Its precise definition and properties depend on concepts from exterior differential systems, which I will explain as needed. An example of a quasi-integrable structure is the standard almost complex structure on the 6-sphere, but there are many others.

I will also examine global conditions and restrictions, an analog of the Hermitian-Einstein condition, and some existence theorems that relate to previous work of mine on almost complex curves in the 6-sphere.

Date received: May 28, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cadq-69.