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Harmonic coordinates

In Riemannian geometry, a branch of mathematics, harmonic coordinates are a certain kind of coordinate chart on a smooth manifold, determined by a Riemannian metric on the manifold. They are useful in many problems of geometric analysis due to their regularity properties. In two dimensions, certain harmonic coordinates known as isothermal coordinates have been studied since the early 1800s. Harmonic coordinates in higher dimensions were developed initially in the context of Lorentzian geometry and general relativity by Albert Einstein and Cornelius Lanczos (see harmonic coordinate condition). Following the work of Dennis DeTurck and Jerry Kazdan in 1981, they began to play a significant role in the geometric analysis literature, although Idzhad Sabitov and S.Z. Šefel had made the same discovery five years earlier.

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Article summary

In Riemannian geometry, a branch of mathematics, harmonic coordinates are a certain kind of coordinate chart on a smooth manifold, determined by a Riemannian metric on the manifold. They are useful in many problems of geometric analysis due to their regularity properties. In two dimensions, certain harmonic coordinates known as isothermal coordinates have been studied since the early 1800s. Harmonic coordinates in higher dimensions were developed initially in the context of Lorentzian geometry and general relativity by Albert Einstein and Cornelius Lanczos (see harmonic coordinate condition). Following the work of Dennis DeTurck and Jerry Kazdan in 1981, they began to play a significant role in the geometric analysis literature, although Idzhad Sabitov and S.Z. Šefel had made the same discovery five years earlier.

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