shape operator
Word Rarity
Uncommon
Frequency: Zipf frequency 4.17 in modern English
20
Scrabble Score
13
Letters
5
Syllables
8
Unique Chars
Meaning
noun
The differential of the Gauss map of an oriented surface at a given point on the surface.
Example Sentences
- "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."
- "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:[…]."
- "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."