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 ... 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 vectors ...
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 ... 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, w (the inner ...

Famous quotes containing the word shape:

    The following general definition of an animal: a system of different organic molecules that have combined with one another, under the impulsion of a sensation similar to an obtuse and muffled sense of touch given to them by the creator of matter as a whole, until each one of them has found the most suitable position for its shape and comfort.
    Denis Diderot (1713–1784)