| 41. | In mathematics, the "'covariant derivative "'is a way of specifying a derivative along tangent vectors of a manifold.
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| 42. | In connection with foliation theory, a subbundle of the tangent bundle of a smooth manifold may be called a distribution ( of tangent vectors ).
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| 43. | For example, the tangent vector is the unit vector perpendicular to in the plane, whose direction is given by the component of perpendicular to.
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| 44. | A "'framing "'of a knot is a choice of a non-tangent vector at each point of the knot.
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| 45. | The above equation holds at each point, and the relation may as well be interpreted as the Minkowski metric at applied to two tangent vectors at.
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| 46. | Therefore, the bracket on " A " is just the Lie bracket of tangent vector fields and the anchor map is just the identity.
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| 47. | A smooth path in a smooth manifold has ( at every point ) the tangent vector, belonging to the tangent space ( attached to this point ).
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| 48. | Is called the unit tangent vector, so an equivalent definition is that the tangential angle at is the angle such that is the unit tangent vector at.
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| 49. | Is called the unit tangent vector, so an equivalent definition is that the tangential angle at is the angle such that is the unit tangent vector at.
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| 50. | Geodesics are said to be time-like, null, or space-like if the tangent vector to one point of the geodesic is of this nature.
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