Five-Dimensional Tangent Vectors in Space-Time: II. Differential-Geometric Approach

Abstract

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 on scalar functions. I then examine their basic algebraic properties and their parallel transport in the particular case where space-time possesses a special local symmetry. After that I give definition to five-dimensional tangent vectors associated with dimensional curve parameters and show that they can be identified with the five-vectors introduced formally in part I (math-ph/9805004). In conclusion I speak about differential forms associated with five-vectors.