curvature form
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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
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 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 — Cur va*ture (k?r v? t?r; 135), n. [L. curvatura. See {Curvate}.] 1. The act of curving, or the state of being bent or curved; a curving or bending, normal or abnormal, as of a line or surface from a rectilinear direction; a bend; a curve. Cowper … The Collaborative International Dictionary of English
Curvature of the spine — Curvature Cur va*ture (k?r v? t?r; 135), n. [L. curvatura. See {Curvate}.] 1. The act of curving, or the state of being bent or curved; a curving or bending, normal or abnormal, as of a line or surface from a rectilinear direction; a bend; a… … The Collaborative International Dictionary of English
Curvature of a measure — In mathematics, the curvature of a measure defined on the Euclidean plane R2 is a quantification of how much the measure s distribution of mass is curved . It is related to notions of curvature in geometry. In the form presented below, 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
curvature — n. 1 the act or state of curving. 2 a curved form. 3 Geom. a the deviation of a curve from a straight line, or of a curved surface from a plane. b the quantity expressing this. Etymology: OF f. L curvatura (as CURVE) … Useful english dictionary
Connection form — In mathematics, and specifically differential geometry, a connection form is a manner of organizing the data of a connection using the language of moving frames and differential forms. Historically, connection forms were introduced by Élie Cartan … Wikipedia
Principal curvature — Saddle surface with normal planes in directions of principal curvatures In differential geometry, the two principal curvatures at a given point of a surface are the eigenvalues of the shape operator at the point. They measure how the surface… … Wikipedia
