Riemannian Geometry as a Field Over Another Geometry
Connor, George Henry, Jr.
Woehler, Karlheinz E.
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The basic tensors of a Riemannian geometry are found in terms of tensor components by considering the geometry as a field over another arbitrary Riemannian geometry. The approach exhibits symmetries not previously noted. In particular the Riemann tensor of a geometry is found to decompose into a sum of tensors, each with the full symmetry of a Riemann tensor, and each dependent upon only one order of derivative of the metric tensor. Further work' to explore the potential value of the approach to general relativity is proposed.
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