shape operator

The shape operatorMathworldPlanetmath S of a surface Σ in 3 is the derivative of the sphere map N:ΣS2 given by N(p)= unit normalMathworldPlanetmath vector fieldMathworldPlanetmath at p. So at each p, S(p)=dpN and it is the linear transformation S(p):TpΣTN(p)S2. This is important, because the determinantMathworldPlanetmath defines the Gaussian curvature at p in Σ.

Title shape operator
Canonical name ShapeOperator
Date of creation 2013-03-22 16:04:31
Last modified on 2013-03-22 16:04:31
Owner juanman (12619)
Last modified by juanman (12619)
Numerical id 6
Author juanman (12619)
Entry type Definition
Classification msc 53A05
Related topic SecondFundamentalForm