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In geometry, a pleated surface is roughly a surface that may have simple folds but is not crumpled in more complicated ways. More precisely, a pleated surface is an isometry from a complete hyperbolic surface ''S'' to a hyperbolic 3-fold such that every point of ''S'' is in the interior of a geodesic that is mapped to a geodesic. They were introduced by , where they were called uncrumpled surfaces. The Universal Book of Mathematics provides the following information about pleated surfaces: ''It is a surface in Euclidean space or hyperbolic space that resembles a polyhedron in the sense that it has flat faces that meet along edges. Unlike a polyhedron, a pleated surface has no corners, but it may have infinitely many edges that form a lami-nation.'' ==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「Pleated surface」の詳細全文を読む スポンサード リンク
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