Alexander Krasulin. Five-dimensional Tangent Vectors in Space-time: Vi. Bivector Derivative and Its Application

Natural Sciences / Mathematics / Geometry

Submitted on: Nov 29, 2012, 04:24:48

Description: In this concluding part of the series I first consider the bivector derivative for four-vector and four-tensor fields in the case of arbitrary Riemannian geometry. I then define this derivative for five-vector and five-tensor fields, examine the bivector analogs of the Riemann tensor, and introduce the notion of the commutator for the fields of five-vector bivectors. After that I examine a more general case of five-vector affine connection, introduce the five-vector analog of the curvature tensor, discuss the canonical stress-energy and angular momentum tensors corresponding to the five-vector covariant derivative, and consider a possible five-vector generalization of the Einstein and Kibble-Sciama equations. In conclusion, I introduce the notion of the bivector derivative for the fields of nonspacetime vectors and tensors, consider the corresponding gauge fields and their properties, and derive a possible generalization of Maxwell's equation.

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