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Gaussian Curvature

Basic definition

Gaussian curvature is one type measure of the amount of "bending" a surface undergoes at a given point which is independent of the coordinate system used to describe it.

Detailed definition

Gaussian curvature, sometimes also called total curvature, is an intrinsic property of a space independent of the coordinate system used to describe it. The Gaussian curvature of a regular surface in R^3 at a point p is formally defined as
K(p) = det(S(p)), where S is the shape operator and det denotes the determinant.

Related terms

anticlastic | Brioschi formula | developable surface | elliptic point | hyperbolic point | integral curvature | mean curvature | metric tensor | minimal surface | parabolic point | planar point | scalar curvature | synclastic | total curvature | umbilic point

Educational grade level

college level

Associated person

Carl Friedrich Gauss

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