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 {\it CR} dimension one, with arbitrary {\it CR} codimension. Next we pass to Lorenzian structures with any {\it CR} codimension and {\it CR} dimension . 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