viii CONTENT S
1. Je t bundle s o f infinite orde r 6 7
2. Th e tautologica l variationa l bi-comple x o n J°°{E) 6 9
Chapter 8 . Th e invers e proble m o f the calculu s o f variations 7 5
1. Th e local , globa l an d equivarian t invers e problem s 7 5
2. Edg e complexe s an d obstruction s 7 8
3. Variationa l principle s an d symmetr y reductio n 8 1
Chapter 9 . Conservatio n law s and Darbou x integrabilit y 8 3
1. Scala r hyperboli c partia l differentia l equation s i n th e plan e 8 3
2. Th e constraine d variationa l bi-comple x 8 5
3. Conservatio n law s 8 6
4. Th e generalize d Laplac e invariant s 8 9
5. Vanishin g theorem s fo r conservatio n law s 9 2
6. Darbou x integrabilit y 9 3
7. Furthe r application s 9 7
Chapter 10. Characteristi c cohomolog y o f differentia l system s 9 9
1. Exterio r differentia l system s 9 9
2. Som e existenc e theorem s fo r integra l manifold s 101
3. Involutiv e system s an d th e Cartan-Kahle r theore m 103
4. Characteristi c cohomolog y 108
Bibliography 111
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