| 11. | All curves through point p have a tangent vector, not only world lines.
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| 12. | This allows tangent vectors to be classified into timelike, null, and spacelike.
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| 13. | The Riemann tensor is a multilinear operator of fourth rank acting on tangent vectors.
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| 14. | This angle is equal to the angle between the tangent vectors to the curves.
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| 15. | Volume forms and tangent vectors can be combined to give yet another description of orientability.
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| 16. | To do this we first define an equivalence relation on pairs of timelike tangent vectors.
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| 17. | The magnitude of the tangent vector,
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| 18. | The unit tangent vector taken as a curve traces the spherical image of the original curve.
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| 19. | Where { \ mathbf T } ( s ) is the tangent vector of the curve.
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| 20. | Such tangent vectors are said to be "'parallel transports "'of each other.
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