Levi-Civita equivariance and Riemann symmetries

Details Levi-Civita equivariance and Riemann symmetries Levi-Civita equivariance and Riemann symmetries

Dec 1994

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994gregr..26.1213s&link_type=abstract

General Relativity and Gravitation, Volume 26, Issue 12, pp.1213-1215

Physics

Scientific paper

We present a novel derivation of all the symmetries of the Riemann curvature tensor. Our approach is entirely geometric, using as it does the natural equivariance of the Levi-Civita map with respect to diffeomorphisms. An important conclusion is thatall symmetries of the curvature tensor have their origin in “the principle of general covariance“.

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