(b) Show that the definition F= VA-VA, which uses the covariant derivative, is equiv- alent to the definition above. Suppose that A,, is a covector field, and consider the object Fμv=O₁ Av - 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= VA-VA, which uses the covariant derivative, is equiv- alent to the definition above. Suppose that A,, is a covector field, and consider the object Fμv=O₁ Av - O₂ A₁. (a) Show explicitly that F is a tensor, that is, show that it transforms appropriately under a coordinate transformation.
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Question
Transcribed Image Text:(b) Show that the definition F= VA-VA, which uses the covariant derivative, is equiv-
alent to the definition above.
Transcribed Image Text:Suppose that A,, is a covector field, and consider the object
Fμv=O₁ Av - O₂ A₁.
(a) Show explicitly that F is a tensor, that is, show that it transforms appropriately under a
coordinate transformation.
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