quadratic differential sentence in Hindi
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- Is invariant under ?, so determine quadratic differentials on " S ".
- These give rise, via the Schwarzian derivative, to quadratic differentials on X.
- In other words, deformations are regulated by holomorphic quadratic differentials on a Riemann surface, again something known classically.
- The Weil Petersson metric is the Riemannian metric defined by the L ^ 2 inner product on quadratic differentials.
- Quadratic differentials on a Riemann surface X are identified with the tangent space at ( X, f ) to Teichm�ller space.
- 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.
- 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.
- 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 ".
- 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 ".
- 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.
- For example, in Riemann surface theory, the deformation theory of complex structures is studied classically by means of quadratic differentials ( namely sections of " L " ( " K " 2 ) ).
- If a point of Teichm�ller space is represented by a Riemann surface " R ", then the cotangent space at that point can be identified with the space of quadratic differentials at " R ".
- According to the definition of a hypercycle, it is a nonlinear, dynamic system, and, in the simplest case, it can be assumed that it grows at a rate determined by a system of quadratic differential equations.
- Since the Riemann surface has a natural hyperbolic metric, at least if it has negative Euler characteristic, one can define a Hermitian inner product on the space of quadratic differentials by integrating over the Riemann surface.
- As in the case of translation surfaces there is an analytic interpretation : a half-translation surface can be interpreted as a pair ( X, \ phi ) where X is a Riemann surface and \ phi a quadratic differential on X.
- To pass from the geometric picture to the analytic picture one simply takes the quadratic differential defined locally by ( dz ) ^ 2 ( which is invariant under half-translations ), and for the other direction one takes the Riemannian metric induced by \ phi, which is smooth and flat outside of the zeros of \ phi.
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