curvature tensor


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curvature tensor

[′kər·və·chər ‚ten·sər]
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are now the components of the Riemann-Christoffel curvature tensor describing the curvature of space-time in the standard general relativity theory.
This is nothing else but curvature tensor of Q-space built out of proper Q-connexion components (in their turn being functions of 4D coordinates).
which possesses all the properties of the Riemann-Christoffel curvature tensor [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] in the observer's spatial section, and constructed with the use [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the chr.
By analogy with the Riemann-Christoffel curvature tensor, Zelmanov derived the chr.
2) are the components of a [THETA](4)-invariant tensor field; (b) The curvature tensor, the Ricci tensor, and the scalar curvature related to (2.
Therefore the non-vanishing components of the projective curvature tensor and their covariant derivatives are respectively:
p]M, p [member of] M, by h the second fundamental form and by R the Riemann curvature tensor of M.
In this paper we extend the conservativeness of conformal and Quasi conformal curvature tensor to K-contact manifold admitting semi-symmetric metric connection.
They define a Weil-Petersson metric on T(1) by Hilbert space inner products on tangent spaces, execute its Riemann curvature tensor, and show that T(1) is a Kahler-Einstein manifold with negative Ricci and sectional curvatures.
for any vector fields X, Y, Z, where R and S are the Riemannian curvature tensor and Ricci tensor of the manifolds respectively ([10], [18]).