TITLE:
On the Rotation of a Vector Field in a Four-Dimensional Space
AUTHORS:
Leonardo Simal Moreira
KEYWORDS:
Products of Vectors; Dimensional Analogy; Vector Fields; Curl; Rotations; Curl by Analogy
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.1,
January
10,
2014
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.