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- W2034632598 abstract "The central role of the Riemann curvature tensor in Einstein's gravitational theory, including the significance of its invariant decomposition in spacetime (with respect to the duality and trace operations) into essentially local and non-local parts, is considered in the light of some of the thoughts and contributions of Cornelius Lanczos (1893–1974). Also, in this context, the fundamental role of the embedded two-space elements, specified by simple bivectors, in defining the Riemannian curvatures is briefly investigated. In particular, it is shown that the formulation of a bivector form of geodesic deviation for the Riemannian curvatures elucidates some of the insights of Weyl and Lánczos. Finally, some of Lánczos' thoughts relating to the nature of the essentially local and non-local parts of the Riemann tensor are discussed. These considerations are discussed in terms of Lánczos' discovery (1962) of the existence (in all Riemannian spacetimes) of a third order tensor H ij k that can be regarded as the potential of the non-local (Weyl) part of the Riemann tensor." @default.
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- W2034632598 date "1975-01-01" @default.
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- W2034632598 title "Elucidation of some of Lanczos' thoughts concerning spacetime curvature and the local and non-local parts of the Riemann tensor" @default.
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- W2034632598 doi "https://doi.org/10.1016/0898-1221(75)90036-x" @default.
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