Is invariant under ?, so determine quadratic differentials on " S ".
2.
These give rise, via the Schwarzian derivative, to quadratic differentials on X.
3.
In other words, deformations are regulated by holomorphic quadratic differentials on a Riemann surface, again something known classically.
4.
The Weil Petersson metric is the Riemannian metric defined by the L ^ 2 inner product on quadratic differentials.
5.
Quadratic differentials on a Riemann surface X are identified with the tangent space at ( X, f ) to Teichm�ller space.
6.
Mind you, this is the son who has never made a B in his life, who can explain Einstein's theory of relativity and analyze quadratic differentials.
7.
This implies for instance the generation of the quadratic differentials on such curves by the differentials of the first kind; and this has consequences for the local Torelli theorem.
8.
In this way, the Teichm�ller space of " S " is realized as an open subspace of the finite-dimensional complex vector space of quadratic differentials on " S ".
9.
The name of the society was chosen at random by Higman from the titles of the books; in this case, Oswald Veblen's " Invariants of Quadratic Differential Forms ".
10.
If X is a Riemann surface then the vector space of quadratic differentials on X is naturally identified with the tangent space to Teichm�ller space at any point above X.
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