Constructing involutive tableaux with Guillemin normal form

DOI10.3842/SIGMA.2015.053zbMATH Open1327.58005arXiv1410.7593MaRDI QIDQ887724

Publication date: 27 October 2015

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Abstract: Involutivity is the algebraic property that guarantees solutions to an analytic and torsion-free exterior differential system or partial differential equation via the Cartan-K"ahler theorem. Guillemin normal form establishes that the prolonged symbol of an involutive system admits a commutativity property on certain subspaces of the prolonged tableau. This article examines Guillemin normal form in detail, aiming at a more systematic approach to classifying involutive systems. The main result is an explicit quadratic condition for involutivity of the type suggested but not completed in Chapter IV, S 5 of the book Exterior Differential Systems by Bryant, Chern, Gardner, Goldschmidt, and Griffiths. This condition enhances Guillemin normal form and characterizes involutive tableaux.

Full work available at URL: https://arxiv.org/abs/1410.7593

File on IPFS (Hint: this is only the Hash - if you get a timeout, this file is not available on our server.)

zbMATH Keywords

exterior differential systems symbol tableau involutivity Guillemin normal form

Mathematics Subject Classification ID

Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks, etc.) (58H10) Exterior differential systems (Cartan theory) (58A15)

This page was built for publication: Constructing involutive tableaux with Guillemin normal form

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q887724)