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

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