Regularity of sections of CR vector bundles

Abstract

In this note, we show that every generalized section σ \sigma of a CR vector bundle E E over a CR manifold M M has the property that near most points of its singular support, there exists a proper abstract CR subbundle F ⊂ E F \subset E which has the property that every real subbundle of E E which contains the image of σ \sigma also contains F F .