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Что (кто) такое curvature tensor - определение
WIKIMEDIA DISAMBIGUATION PAGE
Curvature tensor (disambiguation); Curvature tensors
Riemann curvature tensor
TENSOR FIELD IN GENERAL RELATIVITY AND GEOMETRY
Riemanian curvature; Riemann tensor; Riemann tensor (general relativity); Riemann-Christoffel curvature tensor; Riemann-Christoffel tensor; Riemannian curvature; Riemann–Christoffel tensor; Riemannian curvature tensor; Riemann–Christoffel curvature tensor; Riemannian space-time
In the mathematical field of differential geometry, the Riemann curvature tensor or Riemann–Christoffel tensor (after Bernhard Riemann and Elwin Bruno Christoffel) is the most common way used to express the curvature of Riemannian manifolds. It assigns a tensor to each point of a Riemannian manifold (i.
Weyl tensor
MEASURE OF THE CURVATURE OF A PSEUDO-RIEMANNIAN MANIFOLD
Conformal tensor; Weyl curvature tensor; Weyl curvature
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 manifold. Like the Riemann curvature tensor, the Weyl tensor expresses the tidal force that a body feels when moving along a geodesic.
Ricci curvature
2-TENSOR OBTAINED AS A CONTRACTION OF THE RIEMAN CURVATURE 4-TENSOR ON A RIEMANNIAN MANIFOLD (OR, MORE GENERALLY, A SMOOTH MANIFOLD EQUIPPED WITH AFFINE CONNECTION)
Ricci-curvature; Ricci curvature tensor; Ricci tensor; Trace-free Ricci tensor; Ricci form; Ricci Curvature
In differential geometry, the Ricci curvature tensor, named after Gregorio Ricci-Curbastro, is a geometric object which is determined by a choice of Riemannian or pseudo-Riemannian metric on a manifold. It can be considered, broadly, as a measure of the degree to which the geometry of a given metric tensor differs locally from that of ordinary Euclidean space or pseudo-Euclidean space.
Википедия
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 curvature form of an Ehresmann connection: see Ehresmann connection, connection (principal bundle) or connection (vector bundle). It is the one of the numbers that are important in the Einstein field equations.
