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On the Rotation of a Vector Field in a Four-Dimensional Space

DOI: 10.4236/am.2014.51015, PP. 128-136

Keywords: Products of Vectors, Dimensional Analogy, Vector Fields, Curl, Rotations, Curl by Analogy

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Abstract:

Recently I published a paper in the journal ALAMT (Advances in Linear Algebra & Matrix Theory) and explored the possibility of obtaining products of vectors in dimensions higher than three [1]. In continuation to this work, it is proposed to develop, through dimensional analogy, a vector field with notation and properties analogous to the curl, in this case applied to the space IR4. One can see how the similarities are obvious in relation to the algebraic properties and the geometric structures, if the rotations are compared in spaces of three and four dimensions.

References

[1]  L. Simal Moreira, “Geometric Analogy and Products of Vectors in n Dimensions,” Advances in Linear Algebra & Matrix Theory, Vol. 3, No. 1, 2013, pp. 1-6.
http://dx.doi.org/10.4236/alamt.2013.31001
[2]  M. R. Spiegel, S. Lipschutz and J. Liu, “Mathematical Handbook of Formulas and Tables,” 3rd Edition, Schaum’s Outline Series, McGraw-Hill, New York, 2009.
[3]  F. N. Cole, “On Rotations in Space of Four Dimensions,” American Journal of Mathematics, Vol. 12, No. 2, 1890, pp. 191-210.
http://www.jstor.org/stable2369715
[4]  H. P. Manning, “Geometry of Four Dimensions,” Dover Publications, Mineola, 1956.

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