PlanetMath (more info)
 Math for the people, by the people.
Encyclopedia | Requests | Forums | Docs | Wiki | Random | RSS  
Login
create new user
name:
pass:
forget your password?
Main Menu
Owner confidence rating: Very high Entry average rating: No information on entry rating
Gaussian curvature (Definition)

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

$\displaystyle K = \kappa_1 \kappa_2 $
of the two principal curvatures of the surface at $ p$.

The arithmetic mean of the principal curvatures at a point $ p$

$\displaystyle H = \frac{\kappa_1 + \kappa_2}{2} $
is called the mean curvature of the surface at $ p$.



"Gaussian curvature" is owned by Mathprof.
(view preamble)

View style:

See Also: mean curvature at surface point

Other names:  total curvature, total normal curvature
Also defines:  mean curvature
Log in to rate this entry.
(view current ratings)

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:
AMS MSC53A05 (Differential geometry :: Classical differential geometry :: Surfaces in Euclidean space)

Pending Errata and Addenda
None.
Discussion
Style: Expand: Order:
forum policy

No messages.

Interact
post | correct | update request | add derivation | add example | add (any)