Tohoku Mathematical Journal

Normal coordinate systems from a viewpoint of real analysis

Norio Shimakura

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Normal coordinate systems for pseudo-Riemannian metrics are investigated from a viewpoint of the theory of partial differential equations. Given a cartesian coordinate system $x$, a local metric for which $x$ is a normal coordinate system is determined by a metric tensor at the origin and any one of certain three matrix functions. These are related one another by three partial differential equations. Solvability of these equations in $C^{\infty}$ framework and power series expansion of solutions are discussed.

Article information

Tohoku Math. J. (2), Volume 52, Number 4 (2000), 533-553.

First available in Project Euclid: 3 May 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53B30: Lorentz metrics, indefinite metrics
Secondary: 53B20: Local Riemannian geometry


Shimakura, Norio. Normal coordinate systems from a viewpoint of real analysis. Tohoku Math. J. (2) 52 (2000), no. 4, 533--553. doi:10.2748/tmj/1178207754.

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