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On generalized Cauchy Riemann equations on manifolds. (English) Zbl 0575.32028
This is a research announcement, without proofs, of results concerning a generalization of $$\partial$$, $${\bar \partial}$$ on a Riemann surface to higher dimensional manifolds. The point is that the generalization applies to other than complex manifolds. The concept that replaces ”almost complex structure” is splitting of a vector-valued de Rham sequence.
The authors give several nice applications of their ideas which provide good motivation for the work.
Reviewer: S.G.Krautz

##### MSC:
 32K99 Generalizations of analytic spaces 32L10 Sheaves and cohomology of sections of holomorphic vector bundles, general results 58A10 Differential forms in global analysis 58A12 de Rham theory in global analysis 35N15 $$\overline\partial$$-Neumann problems and formal complexes in context of PDEs 58J10 Differential complexes 53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.) 14F40 de Rham cohomology and algebraic geometry