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

Tags

DTIC Thesaurus Topics

  • General Relativity
  • Geometry
  • Mathematics
  • Symmetry

Readers

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