| 41. | One alternative notation for the covariant derivative of any tensor is the subscripted nabla symbol \ nabla _ \ beta.
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| 42. | Again the covariant derivative is defined like the supercharge but with the second term negated and it anticommutes with the supercharges.
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| 43. | These can be defined directly from the induced covariant derivative " on T " M " as follows.
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| 44. | In physics, connection forms are also used broadly in the context of gauge theory, through the gauge covariant derivative.
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| 45. | Invariants constructed using covariant derivatives up to order n are called n-th order " differential invariants ".
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| 46. | Covariant derivatives are denoted either by the operator \ nabla _ { i } or by subscripts preceded by a semicolon.
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| 47. | Although other covariant derivatives may be supported within the metric, usually one only ever considers the metric-compatible one.
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| 48. | In nonabelian Yang Mills theories, DF = 0 and D * F = 0 where D is the exterior covariant derivative.
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| 49. | Thus a covariant derivative is a way of specifying a derivative of a vector field along another vector field on a manifold.
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| 50. | In this case the Euclidean derivative is broken into two parts, the extrinsic normal component and the intrinsic covariant derivative component.
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