nLab quadratic differential

Idea

A quadratic differential (see Strebel 1984) on a Riemann surface $\Sigma$ is a section of the second symmetric power of the canonical line bundle.

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Related concepts

• Hilbert uniformization

• Witten conjecture

• moduli space of Riemann surfaces

References

Textbook account:

• Kurt Strebel, Quadratic differentials, Springer Verlag, Berlin, 1984 (doi:10.1007/978-3-662-02414-0)

See also:

• Wikipedia, Quadratic differential

• John Hubbard, Howard Masur, Quadratic differentials and foliations, Acta Math. 142: 221-274 (1979) (doi:10.1007/BF02395062)

Specifically on Strebel differentials:

• Philip Tynan, Explicit Examples of Strebel Differentials (arXiv:0910.4752)