Shape Operator

Some articles on shape operator, operator:

Two Dimensions: Curvature of Surfaces - Second Fundamental Form
... A related notion of curvature is the shape operator, which is a linear operator from the tangent plane to itself ... When applied to a tangent vector X to the surface, the shape operator is the tangential component of the rate of change of the normal vector when moved along a curve on the surface tangent to X ... The principal curvatures are the eigenvalues of the shape operator, and in fact the shape operator and second fundamental form have the same matrix representation with respect to a pair of orthonormal ...
Differential Geometry Of Surfaces - Local Metric Structure - Shape Operator
... Further information Peterson operator The differential df of the Gauss map f can be used to define a type of extrinsic curvature, known as the shape operator or ... This operator first appeared implicitly in the work of Wilhelm Blaschke and later explicitly in a treatise by Burali-Forti and Burgati ... point x of the surface, the tangent space is an inner product space, the shape operator Sx can be defined as a linear operator on this space by the formula for ...

Famous quotes containing the word shape:

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    George Chauncey, U.S. educator, author. Gay New York: Gender, Urban Culture, and the Making of the Gay Male World, 1890-1940, p. 1, Basic Books (1994)