1998/04/16 by Alexander Krasulin, Krasulin, Alexander
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geophysics and Gravity Measurements #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Relativity and Gravitational Theory #gr-qc #hep-th #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.math-ph/9804011
25 pages, no figures, LaTex
arxiv created 1998/04/16 · openalex publication_date 1998/04/16 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This article is a summary of a series of papers to be published where I examine a special kind of geometric objects that can be defined in space-time --- five-dimensional tangent vectors. Similar objects exist in any other differentiable manifold, and their dimension is one unit greater than that of the manifold. Like ordinary tangent vectors, the considered five-dimensional vectors and the tensors constructed out of them can be used for describing certain local quantities and in this capacity find direct application in physics. For example, such familiar physical quantities as the stress-energy and angular momentum tensors prove to be parts of a single five-tensor. In this paper I describe several different mathematical definitions of five-dimensional tangent vectors, discuss their basic algebraic and differential properties, and speak about their possible application in the theory of gravity and in gauge theories.