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February 26th, 2014, 06:07 AM  #1 
Senior Member Joined: Nov 2013 Posts: 137 Thanks: 1  Definition for shape operator
In wolframpage there is follows definition for shape operator in a given point by vector v: I think that this equation means: correct, or not? If yes, of according with the matrix calculus (https://en.wikipedia.org/wiki/Matrix...ayout_notation) the derivative of a vector in the space wrt another vector in the space results in a 3x3 matrix: But, the shape operator is a 2x2 matrix. Conclusion, there is something wrong in my interpretation, what is? 

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