Curvature (mathematics)

thumb|A migrating wild-type Dictyostelium discoideum cell whose boundary is colored by curvature. Scale bar: 5 μm.

point on a continuously differentiable plane curve at which the curve crosses its tangent, that is, the curve changes from being concave to convex, or vice versa

tensor field in general relativity and geometry

radius of a circle which best approximates a curve in a given point

2-tensor obtained as a contraction of the Riemann curvature 4-tensor on a Riemannian manifold (or, more generally, a smooth manifold equipped with affine connection)

formulas in differential geometry

in differential geometry, an extrinsic measure of curvature of a surface

mathematical measure of how much a curve twists

at a given point of a surface, one of the two eigenvalues of the shape operator at the point

(1,2)-tensor field associated to an affine connection; characterizes "twist" of geodesics; if nonzero, geodesics will be helices

quadratic form related to curvatures of surfaces

alt=Visualisation of parallel transport on a sphere|thumb|Parallel transport on a sphere along a piecewise smooth path. The initial vector is labelled as V, parallel transported along the curve, and the resulting vector is labelled as \mathcal{P}_{\gamma}(V). The outcome of parallel transport will be different if the path is varied.

Natural moving frame in differential geometry of surfaces

integral of curvature along a curve taken with respect to arc length

Fundamental formulas linking the metric and curvature tensor of a manifold