## Tohoku Mathematical Journal

### Normal coordinate systems from a viewpoint of real analysis

Norio Shimakura

#### Abstract

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

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

Dates
First available in Project Euclid: 3 May 2007

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1178207754

Digital Object Identifier
doi:10.2748/tmj/1178207754

Mathematical Reviews number (MathSciNet)
MR1793935

Zentralblatt MATH identifier
1004.53028

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

#### Citation

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. https://projecteuclid.org/euclid.tmj/1178207754

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