%0 Journal Article %1 Nester200740 %A Nester, James M %D 2007 %J J. Phys. A: Math. Theor. %K imported %P 2751 %T Riemann normal coordinates: a complete accounting %V 40 %X 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=\n2\(n+k-1)!(n-2)!\(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.

@article{Nester200740, 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.}, added-at = {2014-09-15T08:49:36.000+0200}, author = {Nester, James M}, biburl = {https://www.bibsonomy.org/bibtex/27feb8e29f202438ad947039190486fe3/zhaozhh02}, file = {Nester200740.pdf:Nester200740.pdf:PDF}, interhash = {95d5575f66f43465c7038bbd2c9f6e87}, intrahash = {7feb8e29f202438ad947039190486fe3}, journal = {J. Phys. A: Math. Theor.}, keywords = {imported}, owner = {zhao}, pages = 2751, timestamp = {2014-09-15T08:49:36.000+0200}, title = {Riemann normal coordinates: a complete accounting}, volume = 40, year = 2007 }