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Donev and Tashkova [20] have also developed this within a field variables approach to luminally propagating bivector fields.
When grade is 0,1, 2, 3, 4, and 5, the corresponding blade is scalar, vector, bivector, trivector, quadvector, and pseudoscalar, respectively [29].
may be expanded in any given bivector basis and two-form basis as 6 x 6 matrices, each involving 36 scalar parameters in the general case [18].
A bivector extended by a third vector, (a [and] b) [and] c, is a directed volume element called a trivector.
In particular, it was shown that a Riemannian submanifold is totally geodesic iff the metric is soldered to the submanifold and that a submanifold of a Poisson manifold is a (totally) Dirac submanifold iff there exists a normalization such that the Poisson bivector field is soldered to the submanifold with respect to this normalization.
We take [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] to be a bivector space of bifunctions on [H.
In the approach of geometric algebra, using multivector valued Lagrangian, the angular momentum of this internal rotation represents particle spin and it has been explicitly shown as a bivector quantity representing the orientation of the plane of rotation [7,8].
Notice that in [7]and[8] various bispaces, such as bigroup, bisemigroup, biquasigroup, biloop, bigroupoid, biring, bisemiring, bivector, bisemivector, binear-ring, .
We identify the time-like bivector formed by the basis vectors of the Euclidean plan with the time-like basis vector of the Minkowskian plane and identify the space-like bivector formed by the basis vectors of the Minkowskian plane with one of the space-like basis vectors of the Euclidean plane.
However, the angular momentum is basically a planar quantity and better defined as a bivector in a plane [35].
A set of tensor fields located in an n-dimensional Riemannian space is known as a bivector set, and its representation at a point is known as a local bivector set.