• Corpus ID: 17147453

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}
}
  • A. Krasulin
  • Published 16 April 1998
  • Physics
  • arXiv: Mathematical Physics
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… 
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References

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

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

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

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

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

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