pseudo-Riemannian geometry, curvature invariants are scalar quantities constructed from tensors that represent curvature. These tensors are usually the...

general relativity, curvature invariants are a set of scalars formed from the Riemann, Weyl and Ricci tensors — which represent curvature, hence the name...

field tensor Curvature invariant, for curvature invariants in Riemannian and pseudo-Riemannian geometry in general Curvature invariant (general relativity)...

bi-invariant (that is, simultaneously left- and right-invariant). All left-invariant metrics have constant scalar curvature. Left- and bi-invariant metrics...

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...

curvature of Riemannian manifolds. It assigns a tensor to each point of a Riemannian manifold (i.e., it is a tensor field). It is a local invariant of...

The scale-invariant feature transform (SIFT) is a computer vision algorithm to detect, describe, and match local features in images, invented by David...

scalar curvatures become average values (rather than sums) of sectional curvatures. It is a fundamental fact that the scalar curvature is invariant under...

translational symmetry are invariant under certain translations. The integral ∫ M K d μ {\textstyle \int _{M}K\,d\mu } of the Gaussian curvature K {\displaystyle...

physical only after integrating around a closed path, the Berry curvature is a gauge-invariant local manifestation of the geometric properties of the wavefunctions...

Gaussian curvature of a surface does not change if one bends the surface without stretching it. Thus the Gaussian curvature is an intrinsic invariant of a...

In differential geometry, the Ricci curvature tensor, named after Gregorio Ricci-Curbastro, is a geometric object which is determined by a choice of Riemannian...

second invariant means that some observers measure no gravitomagnetism, which is consistent with what was just said. The fact that the first invariant (the...

to topological invariants and knot type. An old result in this direction is the Fáry–Milnor theorem states that if the total curvature of a knot K in...

theory of physics, a Lorentz scalar is a scalar expression whose value is invariant under any Lorentz transformation. A Lorentz scalar may be generated from...

Look up affine in Wiktionary, the free dictionary. The principal curvature-based region detector, also called PCBR is a feature detector used in the fields...

This relationship between a local geometric invariant, the curvature, and a global topological invariant, the index, is characteristic of results in higher-dimensional...

constraint: its trace (as used to define the Ricci curvature) must vanish. The Weyl tensor is invariant with respect to a conformal change of metric: if...

differential-geometric invariants called the curvature and the torsion of a curve. The fundamental theorem of curves asserts that the knowledge of these invariants completely...

states. In mathematics, it has been used to calculate knot invariants and three-manifold invariants such as the Jones polynomial. Particularly, Chern–Simons...

exactly computable Yamabe invariant, and that any Kähler–Einstein metric of negative scalar curvature realizes the Yamabe invariant in dimension 4. It was...

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...

curvature of a surface through p determined by the image under expp of a 2-dimensional subspace of TpM. In the case of Lie groups with a bi-invariant...

property of space and time or four-dimensional spacetime. In particular, the curvature of spacetime is directly related to the energy and momentum of whatever...

p-curvature is an invariant of a connection on a coherent sheaf for schemes of characteristic p > 0. It is a construction similar to a usual curvature,...

coordinate: that is, both the Laplace–Beltrami operator and the curvature are invariant under isometries. Thus, for example, let S be a Riemann surface...

In mathematics, and especially gauge theory, Seiberg–Witten invariants are invariants of compact smooth oriented 4-manifolds introduced by Edward Witten (1994)...

topological invariant cannot change into each other without a phase transition. The topological invariant is constructed from a curvature function that...

mathematical physics, vanishing scalar invariant (VSI) spacetimes are Lorentzian manifolds with all polynomial curvature invariants of all orders vanishing. Although...

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