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In Riemannian geometry and pseudo-Riemannian geometry, curvature invariants are scalar quantities constructed from tensors that represent curvature. These tensors are usually the Riemann tensor, the Weyl tensor, the Ricci tensor and tensors formed from these by the operations of taking dual contractions and covariant differentiations.
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pseudo-Riemannian geometry, curvatureinvariants are scalar quantities constructed from tensors that represent curvature. These tensors are usually the...
field tensor Curvatureinvariant, for curvatureinvariants in Riemannian and pseudo-Riemannian geometry in general Curvatureinvariant (general relativity)...
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...
scalar curvatures become average values (rather than sums) of sectional curvatures. It is a fundamental fact that the scalar curvature is invariant under...
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...
the weak field expression of the invariant interval, Einstein calculated an exactly equal but opposite sign curvature in its spatial components.: 234–238 ...
physical only after integrating around a closed path, the Berry curvature is a gauge-invariant local manifestation of the geometric properties of the wavefunctions...
In differential geometry, the Ricci curvature tensor, named after Gregorio Ricci-Curbastro, is a geometric object which is determined by a choice of Riemannian...
This relationship between a local geometric invariant, the curvature, and a global topological invariant, the index, is characteristic of results in higher-dimensional...
expression, formed from items of the theory, which evaluates to a scalar, invariant under any Lorentz transformation. A Lorentz scalar may be generated from...
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...
exactly computable Yamabe invariant, and that any Kähler–Einstein metric of negative scalar curvature realizes the Yamabe invariant in dimension 4. It was...
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...
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...
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...
The corresponding density is local, and therefore is a Riemannian curvatureinvariant. In particular, whereas the functional determinant itself is prohibitively...
mathematical physics, vanishing scalar invariant (VSI) spacetimes are Lorentzian manifolds with all polynomial curvatureinvariants of all orders vanishing. Although...
topological invariant cannot change into each other without a phase transition. The topological invariant is constructed from a curvature function that...
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