The contorsion tensor (or contortion tensor) in differential geometry is the difference between a connection with and without torsion in it. It commonly...

differential geometry, the torsion tensor is a tensor that is associated to any affine connection. The torsion tensor is a bilinear map of two input vectors...

to: Contortion, a performance art Contorsion, a concept in differential geometry described by the Contorsion tensor an old term for complicated geological...

connection in such a frame, and the Levi-Civita connection is known as the contorsion tensor. When we choose the basis Xi ≡ ui orthonormal: gab ≡ ηab = ⟨Xa, Xb⟩...

connection Levi-Civita connection Ricci calculus Supergravity Torsion tensor Contorsion tensor Dirac equation in curved spacetime M.B. Green, J.H. Schwarz, E...

formulation of spin (the spin tensor). These extra equations express the torsion linearly in terms of the spin tensor associated with the matter source...

\omega _{\mu ab}(e)} , while K μ a b {\displaystyle K_{\mu ab}} is the contorsion tensor. Meanwhile, D ν ( ω ) {\displaystyle D_{\nu }(\omega )} is the covariant...

{\displaystyle d\sigma ^{a}+\omega ^{ab}\wedge \sigma ^{c}\eta _{bc}=0} The contorsion tensor gives the difference between a connection with torsion, and a corresponding...

(with torsion) and the corresponding Levi-Civita connection is the contorsion tensor. The fundamental theorem asserts both existence and uniqueness of...

connection and the corresponding Levi-Civita connection is given by the contorsion tensor. The exterior derivative is a flat connection on E = M × R {\displaystyle...

given by the contorsion tensor. In component notation, the covariant derivative ∇ {\displaystyle \nabla } is compatible with the metric tensor g a b {\displaystyle...

given connection ω, there is a unique one-form σ on TE, called the contorsion tensor, that is vanishing in the vertical bundle, and is such that ω+σ is...

Riemannian connection and its associated Levi-Civita connection is the contorsion tensor. A more specific type of connection form can be constructed when the...

\alpha }+\Gamma _{\mu \nu \alpha }+\Gamma _{\mu \alpha \nu }} and a contorsion tensor S μ ν α = − S μ α ν = 1 2 ( T ν μ α + T ν α μ + T μ ν α + C α ν μ...

solder form on a vector bundle allows one to define the torsion and contorsion tensors of a connection. Solder forms occur in the sigma model, where they...

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