# Orthogonality of Absolute Derivative

1. Jun 16, 2012

### rbwang1225

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.

2. Jun 16, 2012

### rbwang1225

Oh! I am very sorry. It's very straight forward. Since $t^At_A=1, Dt^A/dst_A=0$

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