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Relation between Frenet-Serret torsion and the torsion tensor?

  1. Apr 10, 2010 #1
    Hi, I was wondering if anyone could help me with this differential geometry question I've been struggling to find information on.

    I (at least very roughly) understand the relationship between the Frenet-Serret curvature of a curve and the Riemann curvature of a general n-dimensional manifold: the curvature tensor is determined by the sectional curvatures of 2-D slices through the manifold, and Gauss's theorem relates these sectional curvatures to the curvature of curves along the two principal directions of the 2-D surface.

    What I was wondering was is there a similar geometric relationship between the Frenet-Serret torsion of curves and the torsion tensor for a general manifold, and if so are there any good sources for reading about it?

  2. jcsd
  3. Apr 13, 2010 #2
    ah beginning to see where to start looking. I have Aminov's 'Geometry of Submanifolds' and may also brave Spivak volume 3 or 4 for more on submanifolds... any other suggestions welcome
  4. Apr 17, 2010 #3
    Despite the name, both curvature and torsion of the curve are related to the curvature. I particularly like the approach with differential forms
    but it is probably the best one to start with
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