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v t e Various notions of curvature defined in differential geometry
Differential geometry of curves	Curvature Torsion of a curve Frenet–Serret formulas Radius of curvature (applications) Affine curvature Total curvature Total absolute curvature
Differential geometry of surfaces	Principal curvatures Gaussian curvature Mean curvature Darboux frame Gauss–Codazzi equations First fundamental form Second fundamental form Third fundamental form
Riemannian geometry	Curvature of Riemannian manifolds Riemann curvature tensor Ricci curvature Scalar curvature Sectional curvature
Curvature of connections	Curvature form Torsion tensor Cocurvature Holonomy