Peng, L. & Yang, L. Approx. Theory & its Appl. (1999) 15: 66. doi:10.1007/BF02837124
In higher dimensional spacesRn(n>3) the usual curl does not have the properties as inR3. In this paper, we established the natural concept of curl inR7 via octonion O. We prove that there exists the curl inRn if and only if n=3,7. Some applications are presented, such as the new phenomenon of the differential forms inR7 which is different from the ordinary de Rham cohomology and Hodge theory, grad-curl-div type Dirac operator inR6, seven dimensional Maxwell equations and Navier-Stokes equations.