### Some articles on *shape operator, operator*:

Two Dimensions: Curvature of Surfaces - Second Fundamental Form

... A related notion of curvature is the

... 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 -

... Further information Peterson

**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)

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