PlanetMath: Gaussian curvature

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Gaussian curvature

(Definition)

The Gaussian curvature of a surface at a point is the product

$\displaystyle K = \kappa_1 \kappa_2$

of the two principal curvatures of the surface at

The arithmetic mean of the principal curvatures at a point

$\displaystyle H = \frac{\kappa_1 + \kappa_2}{2}$

is called the mean curvature of the surface at

"Gaussian curvature" is owned by Mathprof.

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Other names:

total curvature, total normal curvature

Also defines:

mean curvature

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Cross-references: arithmetic mean, principal curvatures, product, point, surface
There are 9 references to this entry.

This is version 3 of Gaussian curvature, born on 2007-04-29, modified 2007-04-29.
Object id is 9299, canonical name is GaussianCurvature.
Accessed 1494 times total.

Classification:

53A05 (Differential geometry :: Classical differential geometry :: Surfaces in Euclidean space)

Pending Errata and Addenda

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