Non Completely Solvable Systems of Complex First Order PDE's
C. Denson Hill
Stony Brook University, USAMauro Nacinovich
Università di Roma Tor Vergata, Italy
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Abstract
We revisit the lack of local solvability for homogeneous vector fields with smooth complex valued coefficients, in the spirit of Nirenberg's three dimensional example. First we provide a short expository proof, in the case of CR dimension one, with arbitrary CR codimension. Next we pass to Lorenzian structures with any CR codimension and CR dimension . Several different approaches are presented. Finally we discuss the connection with the absence of the Poincare lemma and the failure of local CR embeddability, and present a global example.
Cite this article
C. Denson Hill, Mauro Nacinovich, Non Completely Solvable Systems of Complex First Order PDE's. Rend. Sem. Mat. Univ. Padova 129 (2013), pp. 129–169
DOI 10.4171/RSMUP/129-9