Suppose that A,, is a covector field, and consider the object Fμ = 0μA, O₂ A₁. (a) Show explicitly that F is a tensor, that is, show that it transforms appropriately under a coordinate transformation. (b) Show that the definition F = V₁A - V₂A, which uses the covariant derivative, is equiv- alent to the definition above.
Suppose that A,, is a covector field, and consider the object Fμ = 0μA, O₂ A₁. (a) Show explicitly that F is a tensor, that is, show that it transforms appropriately under a coordinate transformation. (b) Show that the definition F = V₁A - V₂A, which uses the covariant derivative, is equiv- alent to the definition above.
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Transcribed Image Text:Suppose that A is a covector field, and consider the object
Fμ = 0μA, O₂ A₁.
(a) Show explicitly that F is a tensor, that is, show that it transforms appropriately under a
coordinate transformation.
(b) Show that the definition F = V₁A₂-V₂A, which uses the covariant derivative, is equiv-
alent to the definition above.
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