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Some Remarks on the Nijenhuis Tensor

  • A. P. Stone (a1)
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A differential form α of degree r on an n-manifold is exact if there exists a form β of degree r — 1 such that α = dβ and is closed if dα = 0. Since d-d = 0 any exact form is closed. The Poincaré lemma asserts that a closed differential form of positive degree is locally exact. There is also a complex form, proved by Cartan-Grothendieck, of the Poincaré lemma in which the operator d has a decomposition into components and .

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References
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1. Frölicher, A. and Nijenhuis, A., Theory of vector valued differential forms, I, Nederl. Akad. Wetensch. Proc. Ser. A 59 (1956), 338359.
2. Dolbeault, P., Sur la cohomologie des variétés analytiques complexes, C. R. Acad. Sci. Paris Sér A-B 236 (1953), 175177.
3. Nickerson, H. K., On the complex form of the Poincaré lemma, Proc. Amer. Math. Soc. 8 (1958), 183188.
4. Osborn, H.. Les lois de conservation, Ann. Inst. Fourier (Grenoble) 14 (1964), 7182.
5. Stone, A. P., Higher order conservation laws, J. Differential Geometry 8 (1969), 447456.
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Canadian Journal of Mathematics
  • ISSN: 0008-414X
  • EISSN: 1496-4279
  • URL: /core/journals/canadian-journal-of-mathematics
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