Miyuki Koiso

Developable surfaces with curved folds

A developable surface is a surface which is isometric to a planar region, that is, there exists a continuous bijective mapping from the surface to a planar region which preserves the length of every curve. If the considered surface is smooth, then it is developable if and only if its Gaussian curvature vanishes everywhere. Moreover, in this case, the surface can be continuously and isometrically deformed until the planar region. In this talk, we study developable surfaces with curved folds, which are naturally appear as origami works and have many applications in manufacturing objects. We discuss intrinsic and extrinsic singular points (such as vertices and points in edges), curvatures at each singular point, and the existence and nonexistence of continuous isometric deformations from such a surface to a planar region.