shape operator
noun1
Geometry, Mathematics, Sciences The differential of the Gauss map of an oriented surface at a given point on the surface.
Differential geometry
- Gaussian curvature is a prime example; although defined in terms of shape operators, it belongs to this intrinsic geometry, since it passes the test of isometric invariance.1966, Barrett O'Neill, Elementary Differential Geometry, Academic Press, page 304:
- Timelike surfaces have symmetric shape operators which can be put into one of three canonical forms on a fixed tangent space with respect to an orthonormal basis:[…].2006, Balkan Journal of Geometry and Its Applications, volumes 11-12, page 41:
1 more example
- We have already seen that a plane has zero shape operator. Intuitively, since the shape operator detects the change in the unit normal U, a zero shape operator for a surface M should imply that M is a plane. This is verified by the following result.2007, John Oprea, Differential Geometry and Its Applications, Mathematical Association of America, page 85:
- Synonyms
- Weingarten map