JournalsrsmupVol. 129pp. 129–169

Non Completely Solvable Systems of Complex First Order PDE's

  • C. Denson Hill

    Stony Brook University, USA
  • Mauro Nacinovich

    Università di Roma Tor Vergata, Italy
Non Completely Solvable Systems of Complex First Order PDE's cover
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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 {\it CR} dimension one, with arbitrary {\it CR} codimension. Next we pass to Lorenzian structures with any {\it CR} codimension 1\geq 1 and {\it CR} dimension 2\geq 2. Several different approaches are presented. Finally we discuss the connection with the absence of the Poincare lemma and the failure of local {\it 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