Abstract
In higher dimensional spacesR n(n>3) the usual curl does not have the properties as inR 3. In this paper, we established the natural concept of curl inR 7 via octonion O. We prove that there exists the curl inR n if and only if n=3,7. Some applications are presented, such as the new phenomenon of the differential forms inR 7 which is different from the ordinary de Rham cohomology and Hodge theory, grad-curl-div type Dirac operator inR 6, seven dimensional Maxwell equations and Navier-Stokes equations.
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In Memory of Professor M. T. Cheng
Supported by the National Natural Science Foundation of China.
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Peng, L., Yang, L. The curl in seven dimensional space and its applications. Approx. Theory & its Appl. 15, 66–80 (1999). https://doi.org/10.1007/BF02837124
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DOI: https://doi.org/10.1007/BF02837124