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In mathematics, a quadratic differential on a Riemann surface is a section of the symmetric square of the holomorphic cotangent bundle. If the section is holomorphic, then the quadratic differential is said to be holomorphic. The vector space of holomorphic quadratic differentials on a Riemann surface has a natural interpretation as the cotangent space to the Riemann moduli space or Teichmueller space. ==Local form== Each quadratic differential on a domain in the complex plane may be written as where is the complex variable and is a complex valued function on . Such a `local' quadratic differential is holomorphic if and only if is holomorphic. Given a chart for a general Riemann surface and a quadratic differential on , the pull-back defines a quadratic differential on a domain in the complex plane. 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「quadratic differential」の詳細全文を読む スポンサード リンク
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