Non completely solvable systems of complex first order PDE's

DOI10.4171/RSMUP/129-9zbMath1275.35074arXiv1111.1502MaRDI QIDQ361747

Mauro Nacinovich, Clyde Denson Hill

Publication date: 19 August 2013

Published in: Rendiconti del Seminario Matematico della Università di Padova (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1111.1502

zbMATH Keywords

\(CR\) manifoldscomplex vector fieldsfailure of local \(CR\) embeddabilitylack of local solvability

Mathematics Subject Classification ID

Grassmannians, Schubert varieties, flag manifolds (14M15) Linear first-order PDEs (35F05) Simple, semisimple, reductive (super)algebras (17B20) CR structures, CR operators, and generalizations (32V05) Homotopy groups of topological groups and homogeneous spaces (57T20)

Related Items (3)

On the nonvanishing of abstract Cauchy-Riemann cohomology groups ⋮ A stability theorem for projective CR manifolds ⋮ Lorentzian \(CR\) structures and nonembeddability

Cites Work

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• Cauchy-Riemann functions on manifolds of higher codimension in complex space
• Complex vector fields and hypoelliptic partial differential operators
• Embeddability of abstract CR structures and integrability of related systems
• A property of the functions and distributions annihilated by a locally integrable system of complex vector fields
• Sufficient conditions for the extension of CR structures
• Obstructions to generic embeddings
• The Poincare lemma and local embeddability
• A new approach to the local embedding theorem of CR-structures for 𝑛≥4 (the local solvability for the operator \overline∂_{𝑏} in the abstract sense)

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