Some invariant theorems on geometry of Einstein non-symmetric field theory

Liu Shu-Lin and Xu Sen-Lin

International Journal of Mathematics and Mathematical Sciences, 1983, vol. 6, 1-10

Abstract:

This paper generalizes Einstein's theorem. It is shown that under the transformation T Λ : U i k ℓ → U ¯ i k ℓ ≡ U i k ℓ + δ i ℓ Λ k − δ k ℓ Λ i , curvature tensor S k ℓ m i ( U ) , Ricci tensor S i k ( U ) , and scalar curvature S ( U ) are all invariant, where Λ = Λ j d x j is a closed 1 -differential form on an n -dimensional manifold M .

It is still shown that for arbitrary U , the transformation that makes curvature tensor S k ℓ m i ( U ) (or Ricci tensor S i k ( U ) ) invariant T V : U i k ℓ → U ¯ i k ℓ ≡ U i k ℓ + V i k ℓ must be T Λ transformation, where V (its components are V i k ℓ ) is a second order differentiable covariant tensor field with vector value.

Date: 1983
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:140940

DOI: 10.1155/S0161171283000629

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