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Weil–Petersson metric : ウィキペディア英語版 | Weil–Petersson metric In mathematics, the Weil–Petersson metric is a Kähler metric on the Teichmüller space ''T''''g'',''n'' of genus ''g'' Riemann surfaces with ''n'' marked points. It was introduced by using the Petersson inner product on forms on a Riemann surface (introduced by Hans Petersson). ==Definition==
If a point of Teichmüller 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''. 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. This induces a Hermitian inner product on the tangent space to each point of Teichmüller space, and hence a Riemannian metric.
抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)』 ■ウィキペディアで「Weil–Petersson metric」の詳細全文を読む
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