differential geometry, the curvature form describes curvature of a connection on a principal bundle. The Riemann curvature tensor in Riemannian geometry...

In mathematics, curvature is any of several strongly related concepts in geometry that intuitively measure the amount by which a curve deviates from being...

the manifold a symmetric bilinear form (Besse 1987, p. 43). Broadly, one could analogize the role of the Ricci curvature in Riemannian geometry to that of...

introduced an abstract and rigorous way to define curvature for these manifolds, now known as the Riemann curvature tensor. Similar notions have found applications...

f12 = Ez/c, f23 = −Bz, or equivalent definitions. This form is a special case of the curvature form on the U(1) principal bundle on which both electromagnetism...

The main tensorial invariant of a connection form is its curvature form. In the presence of a solder form identifying the vector bundle with the tangent...

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...

In mathematics, the mean curvature H {\displaystyle H} of a surface S {\displaystyle S} is an extrinsic measure of curvature that comes from differential...

In the mathematical field of differential geometry, the Riemann curvature tensor or Riemann–Christoffel tensor (after Bernhard Riemann and Elwin Bruno...

Gaussian curvature or Gauss curvature Κ of a smooth surface in three-dimensional space at a point is the product of the principal curvatures, κ1 and κ2...

Z\right)+R\left(T\left(X,Y\right),Z\right)\right)=0} The curvature form is the gl(n)-valued 2-form Ω = D ω = d ω + ω ∧ ω {\displaystyle \Omega =D\omega =d\omega...

metric whose curvature form ω is positive (since ω is then a Kähler form that represents the first Chern class of L in H2(X, Z)). The Kähler form ω that satisfies...

curvature of an affine connection or covariant derivative (on tensors); the curvature form of an Ehresmann connection: see Ehresmann connection, connection (principal...

geometry, the two principal curvatures at a given point of a surface are the maximum and minimum values of the curvature as expressed by the eigenvalues...

\mathbf {Q} )} can be presented as differential forms which depend polynomially on the curvature form of a vector bundle. This Chern–Weil theory revealed...

(thoracic and sacral curvatures) form during fetal development. The secondary curves develop after birth. The cervical curvature forms as a result of lifting...

mathematical field of Riemannian geometry, the scalar curvature (or the Ricci scalar) is a measure of the curvature of a Riemannian manifold. To each point on a...

equal to the integral of a certain polynomial (the Euler class) of its curvature form (an analytical invariant). It is a highly non-trivial generalization...

strip without its boundary, called an open Möbius strip, can form surfaces of constant curvature. Certain highly symmetric spaces whose points represent lines...

fundamental form Gauss–Codazzi–Mainardi equations Dupin indicatrix Asymptotic curve Curvature Principal curvatures Mean curvature Gauss curvature Elliptic...

and measure the Earth's radius involve either the spheroid's radius of curvature or the actual topography. A few definitions yield values outside the range...

{\displaystyle P\times ^{G}W} . The curvature form of a principal G-connection ω is the g {\displaystyle {\mathfrak {g}}} -valued 2-form Ω defined by Ω = d ω + 1...

defined primarily by its curvature, while the global geometry is characterised by its topology (which itself is constrained by curvature). General relativity...

represented in a parametrized form, and their geometric properties and various quantities associated with them, such as the curvature and the arc length, are...

In differential geometry, the Weyl curvature tensor, named after Hermann Weyl, is a measure of the curvature of spacetime or, more generally, a pseudo-Riemannian...

In Riemannian geometry, the geodesic curvature k g {\displaystyle k_{g}} of a curve γ {\displaystyle \gamma } measures how far the curve is from being...

in terms of connections and curvature representing classes in the de Rham cohomology rings of M. That is, the theory forms a bridge between the areas of...

}\wedge \sigma .} A flat connection is one whose curvature form vanishes identically. The curvature form has a local description called Cartan's structure...

nondegenerate bilinear form over g {\displaystyle {\mathfrak {g}}} (if G is semisimple, the Killing form will do) and F is the curvature form F ≡ d A + A ∧ A...

In differential geometry, a one-form (or covector field) on a differentiable manifold is a differential form of degree one, that is, a smooth section of...