Total Curvature

The term "total curvature" is used in two different ways in differential geometry.

The total curvature, also called the third curvature, of a space curve with line elements ds_N, ds_T, and ds_B along the normal, tangent, and binormal vectors respectively, is defined as the quantity


where kappa is the curvature and tau is the torsion (Kreyszig 1991, p. 47). The term is apparently also applied to the derivative directly ds_N/ds, namely


(Kreyszig 1991, p. 47).

The second use of "total curvature" is as a synonym for Gaussian curvature (Kreyszig 1991, p. 131).

See also

Curvature, Gaussian Curvature, Lancret Equation, Space Curve, Torsion

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Kreyszig, E. Differential Geometry. New York: Dover, 1991.

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Total Curvature

Cite this as:

Weisstein, Eric W. "Total Curvature." From MathWorld--A Wolfram Web Resource.

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