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In mathematics, a Veech surface is a translation surface (''X'',ω) (a Riemann surface ''X'' with a holomorphic 1-form ω) whose group SL(''X'',ω) of affine diffeomorphisms is a lattice in SL2(R) (a discrete subgroup of cofinite volume). The image of SL(''X'',ω) in PSL2(R) is called the Veech group. The Veech dichotomy says that geodesic flow on a Veech surface is either periodic or ergodic. Veech surfaces, the Veech group, and the Veech dichotomy are named after William A. Veech. The group SL2(R) acts on the set of translation surfaces as follows. A translation surface has coordinate maps to the complex numbers, which can be identified with R2 and is therefore acted on by SL2(R). Composing the coordinate charts of a surface with an action of this group gives a new set of coordinate charts for a new translation surface. The group SL(''X'',ω) is the subgroup of SL2(R) fixing the translation surface (''X'',ω). ==References== * * * 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「Veech surface」の詳細全文を読む スポンサード リンク
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