| 31. | This representation of a vector field depends on the coordinate system, and there is a well-defined tangent vector ).
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| 32. | *As indicated previously, the 1-jet of a curve through " p " is a tangent vector.
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| 33. | These basis vectors are by definition the tangent vectors of the curves obtained by varying one coordinate, keeping the others fixed:
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| 34. | At each point in M the timelike tangent vectors in the point's tangent space can be divided into two classes.
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| 35. | Notice that velocity always points in the direction of motion, in other words for a curved path it is the tangent vector.
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| 36. | The sum of two vectors is again a tangent vector to some other curve and the same holds for multiplying by a scalar.
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| 37. | The initial tangent vector is parallel transported to each tangent along the curve; thus the curve is, indeed, a geodesic.
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| 38. | This is an " n "-dimensional Euclidean space consisting of the tangent vectors of the curves through the point.
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| 39. | A four-velocity is thus the normalized future-directed timelike tangent vector to a world line, and is a contravariant vector.
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| 40. | So far a world line ( and the concept of tangent vectors ) has been described without a means of quantifying the interval between events.
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