Orthogonality of Absolute Derivative

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SUMMARY

The discussion centers on the orthogonality of covariant vectors to the absolute derivative of their contravariant counterparts in the context of General Relativity (GR). It is established that the tangent vector of a curve, represented as ##t^A##, is orthogonal to its absolute derivative, expressed mathematically as ##D\lambda^A/dst_A=0##. The conclusion drawn is that since the tangent vector satisfies the condition ##t^At_A=1##, it follows that the derivative ##Dt^A/dst_A=0##, confirming the orthogonality relationship.

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rbwang1225
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Hello!
Is any covariant vector orthogonal to absolute derivative of its contravariant counterpart?
I read a GR book, and it says the tangent vector of a curve is orthogonal to its absolute derivative, that is ##D\lambda^A/dst_A=0##, where ##t^A## is the unit tangent vector of some curve ##\gamma##.

Any comments would be appreciated.
 
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Oh! I am very sorry. It's very straight forward. Since ##t^At_A=1, Dt^A/dst_A=0##
 

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