6 papers · 1 filter
Five-Dimensional Tangent Vectors in Space-Time: V. Generalization of Covariant Derivative
Alexander Krasulin
In this part of the series I discuss the five-vector generalizations of affine connection and gauge fields. I also give definition to the exterior derivative of nonscalar-valued fi…
Five-Dimensional Tangent Vectors in Space-Time: IV. Generalization of Exterior Calculus
Alexander Krasulin
This part of the series is devoted to the generalization of exterior differential calculus. I give definition to the integral of a five-vector form over a limited space-time volume…
Five-Dimensional Tangent Vectors in Space-Time: III. Some Applications
Alexander Krasulin
In this part of the series I show how five-tensors can be used for describing in a coordinate-independent way finite and infinitesimal Poincare transformations in flat space-time.…
Five-Dimensional Tangent Vectors in Space-Time: II. Differential-Geometric Approach
Alexander Krasulin
In this part of the series five-dimensional tangent vectors are introduced first as equivalence classes of parametrized curves and then as differential-algebraic operators that act…
Five-Dimensional Tangent Vectors in Space-Time: I. Introduction and Formal Theory
Alexander Krasulin
In this series of papers 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 di…
Five-Dimensional Tangent Vectors in Space-Time
Alexander Krasulin
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 v…