Adam, ChristophSánchez Guillén, JoaquínWereszczynski, Andrzej2020-06-062020-06-062007Adam, C., Sanchez-Guillen, J., & Wereszczynski, A. (2007). Integrability and Diffeomorphisms on Target Space. Symmetry, Integrability and Geometry: Methods and Applications. 3 (2007), 123, 11 pages1815-0659http://hdl.handle.net/10347/22882We briefly review the concepts of generalized zero curvature conditions and integrability in higher dimensions, where integrability in this context is related to the existence of infinitely many conservation laws. Under certain assumptions, it turns out that these conservation laws are, in fact, generated by a class of geometric target space transformations, namely the volume-preserving dif feomorphisms. We classify the possible conservation laws of field theories for the case of a three-dimensional target space. Further, we discuss some explicit exampleseng© 2007 Christoph Adam, Joaquin Sanchez-Guillen and Andrzej Wereszczynski. This work was published in SIGMA under the terms of the Creative Commons Attribution-ShareAlike Licensehttps://creativecommons.org/licenses/by-sa/2.0/IntegrabilityZero curvatureConservation lawsNonlinear field theoriesjournal article10.3842/SIGMA.2007.123open access