Alexander Krasulin. Five-dimensional Tangent Vectors in Space-time: Ii. Differential-geometric Approach
Submitted on: Jun 11, 2012, 18:02:12
Natural Sciences / Mathematics / Geometry
Description: 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. In conclusion I speak about differential forms associated with five-vectors.
The abstract of this article has been published in the "Intellectual Archive Bulletin" , June 2012, ISSN 1929-1329.
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