shape operator

English

Noun

shape operator (plural shape operators)

(geometry, differential geometry) The differential of the Gauss map of an oriented surface at a given point on the surface.
- 1966, Barrett O'Neill, Elementary Differential Geometry, Academic Press, page 304,
  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.
- 2006, Balkan Journal of Geometry and Its Applications, Volumes 11-12, page 41,
  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: […] .
- 2007, John Oprea, Differential Geometry and Its Applications, Mathematical Association of America, page 85,
  We have already seen that a plane has zero shape operator. Intuitively, since the shape operator detects the change in the unit normal ${\\displaystyle U}$ , a zero shape operator for a surface ${\\displaystyle M}$ should imply that ${\\displaystyle M}$ is a plane. This is verified by the following result.

Synonyms

(differential of a Gauss map): Weingarten map

单词	shape operator
释义	shape operator English Noun shape operator (plural shape operators) (geometry, differential geometry) The differential of the Gauss map of an oriented surface at a given point on the surface. 1966, Barrett O'Neill, Elementary Differential Geometry, Academic Press, page 304, 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. 2006, Balkan Journal of Geometry and Its Applications, Volumes 11-12, page 41, 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: […] . 2007, John Oprea, Differential Geometry and Its Applications, Mathematical Association of America, page 85, We have already seen that a plane has zero shape operator. Intuitively, since the shape operator detects the change in the unit normal ${\\displaystyle U}$ , a zero shape operator for a surface ${\\displaystyle M}$ should imply that ${\\displaystyle M}$ is a plane. This is verified by the following result. Synonyms (differential of a Gauss map): Weingarten map Further reading Differential geometry of surfaces#Shape operator on Wikipedia.Wikipedia Weingarten equations on Wikipedia.Wikipedia
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shape operator

English

Noun

Synonyms

Further reading