- affine curvature
- мат.аффинная кривизна
English-Russian scientific dictionary. 2008.
affine curvature
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Affine curvature — This article is about the curvature of affine plane curves, not to be confused with the curvature of an affine connection. Special affine curvature, also known as the equi affine curvature or affine curvature, is a particular type of curvature… … Wikipedia
Affine geometry of curves — In the mathematical field of differential geometry, the affine geometry of curves is the study of curves in an affine space, and specifically the properties of such curves which are invariant under the special affine group In the classical… … Wikipedia
Curvature — In mathematics, curvature refers to any of a number of loosely related concepts in different areas of geometry. Intuitively, curvature is the amount by which a geometric object deviates from being flat, or straight in the case of a line, but this … Wikipedia
Curvature of Riemannian manifolds — In mathematics, specifically differential geometry, the infinitesimal geometry of Riemannian manifolds with dimension at least 3 is too complicated to be described by a single number at a given point. Riemann introduced an abstract and rigorous… … Wikipedia
Curvature form — In differential geometry, the curvature form describes curvature of a connection on a principal bundle. It can be considered as an alternative to or generalization of curvature tensor in Riemannian geometry. Contents 1 Definition 1.1 Curvature… … Wikipedia
Affine connection — An affine connection on the sphere rolls the affine tangent plane from one point to another. As it does so, the point of contact traces out a curve in the plane: the development. In the branch of mathematics called differential geometry, an… … Wikipedia
Affine focal set — In mathematics, and especially affine differential geometry, the affine focal set of a smooth submanifold M embedded in a smooth manifold N is the caustic generated by the affine normal lines. It can be realised as the bifurcation set of a… … Wikipedia
Curvature tensor — In differential geometry, the term curvature tensor may refer to: the Riemann curvature tensor of a Riemannian manifold see also Curvature of Riemannian manifolds; the curvature of an affine connection or covariant derivative (on tensors); the… … Wikipedia
Curvature collineation — A curvature collineation (often abbreviated to CC) is vector field which preserves the Riemann tensor in the sense that, where Rabcd are the components of the Riemann tensor. The set of all smooth curvature collineations forms a Lie algebra under … Wikipedia
Scalar curvature — In Riemannian geometry, the scalar curvature (or Ricci scalar) is the simplest curvature invariant of a Riemannian manifold. To each point on a Riemannian manifold, it assigns a single real number determined by the intrinsic geometry of the… … Wikipedia
Sectional curvature — In Riemannian geometry, the sectional curvature is one of the ways to describe the curvature of Riemannian manifolds. The sectional curvature K(σp) depends on a two dimensional plane σp in the tangent space at p. It is the Gaussian curvature of… … Wikipedia
