Characteristic cohomology of differential systems. I. General theory

Authors:
Robert L. Bryant and Phillip A. Griffiths

Journal:
J. Amer. Math. Soc. **8** (1995), 507-596

MSC:
Primary 58H10; Secondary 18G40, 58A15, 58A17

DOI:
https://doi.org/10.1090/S0894-0347-1995-1311820-X

MathSciNet review:
1311820

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References | Similar Articles | Additional Information

**[1]**I. Anderson,*The variational bicomplex*, Notes from Dept. of Mathematics at Utah State University, 1990.**[2]**R. Bryant, S. S. Chern, R. Gardner, H. Goldschmidt, and P. Griffiths,*Exterior differential systems*, Math. Sci. Res. Inst. Publ., vol. 18, Springer-Verlag, Berlin and New York, 1991. MR**1083148 (92h:58007)****[3]**R. Bryant,*Metrics with exceptional holonomy*, Ann. of Math. (2)**126**(1987), 525-576. MR**916718 (89b:53084)****[4]**L. Dickey,*On exactness of variational bicomplex*, preprint from the Univ. of Oklahoma, 1991. MR**1188445 (94b:58035)****[5]**I. M. Gelfand and L. Dikii,*Asymptotic behavior of the resolvent of Sturm-Liouville equations and the algebra of Korteweg-de Vries equations*, Uspekhi Mat. Nauk**30**(1975), no. 5, 67-100. MR**0508337 (58:22746)****[6]**R. Harvey and H. B. Lawson,*On boundaries of complex analytic varieties*, I, Ann. of Math. (2)**102**(1975), 223-290. MR**0425173 (54:13130)****[7]**-,*Calibrated geometries*, Acta Math.**148**(1982), 47-157. MR**666108 (85i:53058)****[8]**Yu. I. Manin,*Algebraic aspects of nonlinear differential equations*, J. Soviet Math.**11**(1979), 1-122.**[9]**P. Olver,*Applications of Lie groups to differential equations*, Springer-Verlag, Berlin and New York, 1986. MR**836734 (88f:58161)****[10]**R. Thom,*Remarques sur les problèmes comportant des inéqualities différentielles globales*, Bull. Soc. Math. France**87**(1959), 455-461. MR**0121807 (22:12537)****[11]**T. Tsujishita,*On variational bicomplexes associated to differential equations*, Osaka J. Math.**19**(1982), 311-363. MR**667492 (84b:58105)****[12]**-,*Homological method of computing invariants of systems of differential equations*, Preprint available from Dept. of Mathematics, Osaka Univ., 1991. MR**1109811 (92h:58184)****[13 A]**M. Vinogradov,*The -spectral sequence, Lagrangian formalism and conservation laws*I, II, J. Math. Anal. Appl.**100**(1984), 1-129. MR**739951 (85j:58150a)****[14]**-,*Local symmetries and conservation laws*, Acta Appl. Math.**2**(1984), 21-78. MR**736872 (85m:58192)****[15]**-,*Geometry of nonlinear differential equations*, J. Soviet Math.**17**(1981), 1624-1649.**[16]**R. Bryant and P. Griffiths,*Characteristic cohomology of differential systems*(II):*Conservation laws for a class of parabolic systems*, Duke Math. J. (to appear). MR**1334205 (96d:58158)**

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DOI:
https://doi.org/10.1090/S0894-0347-1995-1311820-X

Article copyright:
© Copyright 1995
American Mathematical Society