1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Shape Operator Symmetry

  1. May 23, 2006 #1
    :confused: Please, help me to solve that task related to Shape Operator.

    We have surface [tex]S[/tex] and its normal [tex]N[/tex]. Alse we have surface patch [tex]r : U -> S[/tex] in local coordinates [tex]r_1, r_2, ..., r_n[/tex]. Shape operator (Weingarten Linear Operator) is defined as follow:
    [tex]L_p : T_{r(p)}S -> T_{r(p)}S[/tex], where [tex]T_{r(p)}S[/tex] - tangent plane to surface.
    It is known that [tex]L_p(w) = -D_vN(p), w \in T_{r(p)}S[/tex].
    It is necessary to proof, that shape operator is symmetrical.

    There is theorem that shows that shape operator is symmetrical [tex]L_p : T_pS -> T_pS, L_p(v)*w = v*L_p(w)[/tex], but on the surface. For patch we need to prof that matrix is symmetrical or something like that..

    Can anyone lead me to right direction?
    Thank you.
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted



Similar Discussions: Shape Operator Symmetry
  1. Spherical symmetry (Replies: 3)

Loading...