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Quadratic differential
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Quadratic differential : ウィキペディア英語版
Quadratic differential
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 U in the complex plane may be written as
f(z) dz \otimes dz where z is the complex variable and
f is a complex valued function on U .
Such a `local' quadratic differential is holomorphic if and only if f is holomorphic.
Given a chart \mu for a general Riemann surface R
and a quadratic differential q on R, the pull-back
(\mu^)^
*(q) 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



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