Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

What is intrinsic derivative?

  1. Jan 18, 2010 #1
    What is it? and How different between intrinsic(absolute) derivative and covariant derivative?

    What is its geometric interpretation?
  2. jcsd
  3. Jan 19, 2010 #2


    User Avatar
    Science Advisor

    If on a manifold you have two vector fields V and W, then you can take the covariant derivative of V wrt W at every point in the manifold. The vector field W can also be thought of as a family of curves whose tangent vectors form W. The absolute derivative of V at any point on a particular curve in that family is the covariant derivative of V wrt W at that point in the curve.

    The geometric idea is that in a vector space, there is an idea of two vectors being parallel. But on a manifold, there is a vector space at each point in the manifold, but there is no predefined notion of vectors at different points on a manifold being parallel. The covariant derivative/absolute derivative defines the notion of "parallel transport" that allows you to say if vectors at two nearby points on a curve are parallel or not.

    I checked the definition on p377 of http://books.google.com/books?id=vQ...D+physics+geometry+liek&source=gbs_navlinks_s.
    Last edited: Jan 19, 2010
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook