0
$\begingroup$

I understand that torsion is a concept specific to three-dimensional spaces. Despite searching on Google, I've struggled to find how to extend the concept of torsion to an n-dimensional space.

Is it not feasible to adapt torsion for higher dimensions, or is there a formula in the academic literature that addresses this? I also looked for references on this topic but couldn't find any.

$\endgroup$
9
  • 1
    $\begingroup$ It is hard to believe that a google search won't find torsion in differential geometry. $\endgroup$
    – Kurt G.
    Commented Feb 28 at 11:26
  • $\begingroup$ @KurtG. Although I agree with you, I'm not sure exactly how torsion for affine connections is linked to the torsion of curves in $\Bbb R^3$, which is what I presume OP refers to $\endgroup$
    – Didier
    Commented Feb 28 at 15:17
  • 1
    $\begingroup$ @AndrewD.Hwang I am rather interested in the torsion of curves in the context of the Frenet Frame $\endgroup$
    – pedro colombino
    Commented Feb 29 at 17:52
  • 1
    $\begingroup$ If memory serves, there is a complete account in either volume 2 or (likelier?) 3 of Spivak's Comprehensive Introduction to Differential Geometry; the general idea is to define (an orthonormal generalization of) the Frenet frame recursively so that the derivative of the unit velocity $e_1$ lies in the plane spanned by $\{e_1, e_2\}$, the derivative of $e_2$ lies in the three-space spanned by $\{e_1, e_2, e_3\}$, and so forth. $\endgroup$
    – Andrew D. Hwang
    Commented Mar 1 at 2:09
  • 1
    $\begingroup$ See this post and particularly this post. $\endgroup$
    – Ted Shifrin
    Commented Mar 5 at 16:13

0

Reset to default

You must log in to answer this question.