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 ... 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 ...
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 Weingarten map ... This operator first appeared implicitly in the work of Wilhelm Blaschke and later explicitly in a treatise by Burali-Forti and Burgati ... Since at each 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 tangent vectors v ...

Famous quotes containing the word shape:

    Somebody once said that I am incapable of drawing a man, but that I draw abstract things like despair, disillusion, despondency, sorrow, lapse of memory, exile, and that these things are sometimes in a shape that might be called Man or Woman.
    James Thurber (1894–1961)