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 >= 1 and CR dimension >= 2. 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.
Hill, C., Nacinovich, M. (2013). Non Completely Solvable Systems of Complex First Order PDE's. RENDICONTI DEL SEMINARIO MATEMATICO DELL'UNIVERSITA' DI PADOVA, 129, 129-169 [10.4171/RSMUP/129-9].
Non Completely Solvable Systems of Complex First Order PDE's
NACINOVICH, MAURO
2013-01-01
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 >= 1 and CR dimension >= 2. 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
