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Orthogonality of Absolute Derivative

  1. Jun 16, 2012 #1
    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. jcsd
  3. Jun 16, 2012 #2
    Oh! I am very sorry. It's very straight forward. Since ##t^At_A=1, Dt^A/dst_A=0##
     
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