Riemannian Geometry as a Field Over Another Geometry.
Abstract
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 one order of derivative of the metric tensor. Further work to explore the potential value of the approach to general relativity is proposed. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1968
- Accession Number
- AD0844151
Entities
People
- George Henry Connor Jr
Organizations
- Naval Postgraduate School