Results 171 to 180 of about 58,187 (222)

Riemann Curvature Tensor

, 2014
Suppose we have a coordinate system \({x}^{\mu }\) in a region of an \(n\)-dimensional Riemann (or pseudo-Riemann) manifold [20]. Components of the metric tensor \(g_{\mu \nu }\) are given as functions of \({x}^{\mu }\). We want to calculate the Riemann curvature tensor \({R}^{\mu }\,_{\nu \alpha \beta }\) and related quantities (the Ricci tensor \(R_{\
A. Grozin
semanticscholar   +3 more sources

The Riemann Curvature Tensor and Higgs Scalar Field within CAM Theory

Advances in Applied Clifford Algebras, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
B. Wolk
semanticscholar   +3 more sources

Riemann curvature tensor and closed geodesic paths

American Journal of Physics, 1977
It is shown how standard treatments of the change in a vector Δξi under parallel transport about a closed path in Riemannian spacetime lead to erroneous results if a complete circuit is made rather than just half a circuit followed by antisymmetrization.
R. E. Morganstern
semanticscholar   +3 more sources

The continuous determination of spacetime geometry by the Riemann curvature tensor

Classical and Quantum Gravity, 1988
This paper continues work of the reviewer and others which studies the following problem: given a manifold M of dimension \(n\geq 4\) with Lorentz metric g and corresponding symmetric connection \(\Gamma\) and Riemann tensor R, to what extent does R determine g and \(\Gamma\) ?
A. Rendall
semanticscholar   +5 more sources

Estimates for the Riemann Curvature Tensor

, 2003
This chapter is devoted to the proof of Theorem M7 in terms of the fundamental quantities Q, \(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{Q} \). These quantities can be expressed, according to (3.5.1), as weighted integrals of the null components of \(\hat L_0 R,\hat L_0 R,\hat L^2 _0 R,\hat L_0 \hat L_T R and \hat L_S \hat L_T R\)along
S. Klainerman, F. Nicoló
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The Algebra of the Riemann Curvature Tensor in General Relativity: Preliminaries

Studies in Applied Mathematics, 1972
In a four‐dimensional curved space‐time it is well‐known that the Riemann curvature tensor has twenty independent components; ten of these components appear in the Weyl tensor, and nine of these components appear in the Einstein curvature tensor. It is also known that there are fourteen combinations of these components which are invariant under local ...
Phillip Greenberg
semanticscholar   +2 more sources

Equivalent Circuits for Oscillating Systems and the Riemann-Christoffel Curvature Tensor

Electrical Engineering, 1943
Not ...
Gabriel Kron
  +6 more sources

The Algebra of the Riemann Curvature Tensor in General Relativity: The Relation of the Invariants of the Einstein Curvature Tensor to the Invariants Describing Matter

Studies in Applied Mathematics, 1972
In this paper, the second in a series of papers on the algebra of the Riemann curvature tensor, we relate the algebraic invariants of the Einstein curvature tensor to the algebraic invariants of the trace‐free part of the Ricci tensor, and, consequently, to the trace‐free part of the stress‐energy tensor for the physical system. We also show explicitly
Phillip Greenberg
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The Riemann and extrinsic curvature tensors in the Regge calculus

Classical and Quantum Gravity, 1988
A detailed analysis of the Riemann tensor in the neighbourhood of one bone and of the extrinsic curvature in the neighbourhood of one triangular face in a simplicial geometry is presented. Unlike most previous analyses this analysis makes no reference to any particular choice of smoothing scheme. Explicit formulae will be presented for both the Riemann
Leo Brewin
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