Foliate partial holomorphic structures on principal bundles

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Abstract

The foliate partial holomorphic (f.p.h.) pseudogroup is the pseudogroup of the local diffeomorphisms of ℝm which preserve a distribution of the form span {Mathematical expression}, where ya are real coordinates, zα are complex coordinates, and ℝm may have also some other real coordinates. The f.p.h. structures on manifolds are described geometrically by the Nirenberg-Frobenius theorem [N], and occur in many interesting situations [R], [FW], [DK1], [V3], etc. The present paper discusses f.p.h. structures on principal bundles, and associates with such structures adapted connections, and forms with values in an associated bundle of Lie algebras.

Original languageEnglish
Pages (from-to)307-321
Number of pages15
JournalMonatshefte fur Mathematik
Volume111
Issue number4
DOIs
StatePublished - Dec 1991

ASJC Scopus subject areas

  • Mathematics (all)

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