A note on a differential concomitant
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- by P. R. Eiseman and A. P. Stone PDF
- Proc. Amer. Math. Soc. 53 (1975), 179-185 Request permission
Abstract:
If ${\mathbf {h}}$ and ${\mathbf {k}}$ are vector $1$-fotms, the vanishing of the concomitant $[{\mathbf {h}},\;{\mathbf {k}}]$ is an integrability condition fot certain problems on manifolds. In the case that ${\mathbf {h}} = {\mathbf {k}}$ the vanishing of the Nijenhuis tensor $[{\mathbf {h}},\;{\mathbf {h}}]$ implies $d(\operatorname {tr} {\mathbf {h}})$ is a conservation law for ${\mathbf {h}}$, provided that $\operatorname {tr} {\mathbf {h}}$ is not constant. When the trace of ${\mathbf {h}}$ is constant, a conservation law for ${\mathbf {h}}$ exists if one can find a vector $1$-form ${\mathbf {k}}$ with nonconstant trace such that $[{\mathbf {h}},\;{\mathbf {k}}] = 0$.References
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Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 53 (1975), 179-185
- MSC: Primary 58A10
- DOI: https://doi.org/10.1090/S0002-9939-1975-0383445-3
- MathSciNet review: 0383445