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Complex spacetime tangent bundle

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Abstract

It is demonstrated that the spacetime tangent bundle, in the case of a Finsler spacetime, is complex, provided that the gauge curvature field vanishes. This is accomplished by determining the conditions for the vanishing of the Nijenhuis tensor in the anholonomic frame adapted to the spacetime connection.

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Brandt, H.E. Complex spacetime tangent bundle. Found Phys Lett 6, 245–255 (1993). https://doi.org/10.1007/BF00665729

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Key words

  • general relativity
  • complex spacetime tangent bundle
  • Finsler spacetime
  • complex analytic manifolds
  • Kähler manifolds
  • maximal proper acceleration