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Journal of Physics A: Mathematical and Theoretical Volume 40 Number 11 Create an alert RSS this journal

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

Riemann normal coordinates: a complete accounting

James M Nester

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Abstract References Cited By

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

02.40.Ky Riemannian geometries

02.40.Hw Classical differential geometry

02.30.Mv Approximations and expansions

02.30.Lt Sequences, series, and summability

MSC

53B21 Methods of Riemannian geometry

58D17 Manifolds of metrics (esp. Riemannian)

41A58 Series expansions (e.g. Taylor, Lidstone series, but not Fourier series)

Subjects

Mathematical physics

Dates

Issue 11 (16 March 2007)

Received 2 January 2007

Published 28 February 2007



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