Isometries between given surfaces and the isometric deformation of a single unstretchable material surface (Q2085531)

The concept of isometry is a well known property in the theory of surfaces (and Riemannian geometry in general). The present paper discusses the difference between the differential geometric concept of an isometry between two given surfaces as purely mathematical objects and the kinematical concept of an isometric deformation of a single unstretchable material surface as a physical object. Further, the authors analyse some misunderstandings that have been promoted in recent works concerning the mechanics of unstretchable material surfaces and discuss this issue within the context of two specific examples. A revealing distinction between isometries and isometric deformations in two space dimensions is reviewed, and the use of rectifying developable surfaces to characterize the isometric deformation of rectangular material strips is presented.