Riemannian Geometry as a Field Over Another Geometry
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...
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| Language: | en_US |
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Monterey, California. Naval Postgraduate School
2013
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| Online Access: | http://hdl.handle.net/10945/28507 |
| Summary: | 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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