Riemann normal coordinates: a complete accounting

doi:10.1088/1751-8113/40/11/010

Riemann normal coordinates: a complete accounting

James M Nester 2007 J. Phys. A: Math. Theor. 40 2751-2754 doi: 10.1088/1751-8113/40/11/010

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James M Nester
Department of Physics and Institute of Astronomy, National Central University, Chungli 32054, Taiwan, Republic of China
E-mail: nester@phy.ncu.edu.tw

Abstract. For the extension of Riemann normal coordinates to higher orders, we show that the amount of geometric information in the kth order for an n-dimensional Riemannian manifold is $F^n_k=\frac n2\frac{(n+k-1)!}{(n-2)!}\frac{(k-1)}{(k+1)!}$ , and we account for this number in terms of the curvature and the Bianchi identities, along with their respective derivatives to various orders.

PACS numbers: 02.40.Hw, 02.40.Ky

Print publication: Issue 11 (16 March 2007)
Received 2 January 2007
Published 28 February 2007

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Riemann normal coordinates: a complete accounting

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