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I have heard that in a space with torsion teleparallel curves and geodesics are different and they coincide when the torsion vanishes. But I couldn't find any definition for the teleparallel curve. Please help.

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  • $\begingroup$ Read WP? Have a look. $\endgroup$ Commented Jun 1, 2020 at 14:47
  • $\begingroup$ @CosmasZachos I saw that but I need the mathematical definition for the teleparallel curve. I can't see the definition of the curve there. $\endgroup$ Commented Jun 1, 2020 at 14:53
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    $\begingroup$ Are you confusing autoparallel with teleparallel? An autoparallel curve has a parallel transported tangent vector. For a torsion-free conection an autoparallel is a geodesic. Otherwise not. "Teleparallel" is something else entirely. $\endgroup$
    – mike stone
    Commented Jun 1, 2020 at 14:58
  • $\begingroup$ @mikestone Thank you for your clarification. Then can you please explain what is teleparallel ? $\endgroup$ Commented Jun 1, 2020 at 15:21
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    $\begingroup$ I think it best to read the links. teleparallel is theory that introduces a global tetrad field, and declares it everywhere parallel -- i.e there is a connection with no curvature. $\endgroup$
    – mike stone
    Commented Jun 1, 2020 at 16:08

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