# Five-Dimensional Tangent Vectors in Space-Time

@article{Krasulin1998FiveDimensionalTV, title={Five-Dimensional Tangent Vectors in Space-Time}, author={Alexander Krasulin}, journal={arXiv: Mathematical Physics}, year={1998} }

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…

## 2 Citations

### Translating the Concept of Five-Dimensional Tangent Vectors in Space-Time to Internal Gauge Symmetries in Elementary Particle Physics

- Physics
- 2013

This paper discusses the analogs of space-time five-dimensional tangent vectors for the case of internal symmetry vector spaces associated with gauge groups in elementary particle physics and their…

### Bivector Gauge Fields and Amplification of Radiation from Distant Cosmic Sources

- Physics
- 2017

This paper describes in some detail the concept of bivector gauge fields and then examines the possibility of confirming their existence by recording certain patterns in variation of intensity of…

## References

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### Five-Dimensional Tangent Vectors in Space-Time: IV. Generalization of Exterior Calculus

- Mathematics
- 1998

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 of appropriate…

### Five-Dimensional Tangent Vectors in Space-Time: V. Generalization of Covariant Derivative

- Mathematics
- 1998

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 five-vector forms and…

### Five-Dimensional Tangent Vectors in Space-Time: III. Some Applications

- Physics
- 1998

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. As an illustration,…

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

- Mathematics
- 1998

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…

### Akad. Wiss. Berlin, Math.–Phys. K1. Z. Phys

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