2001/11/01 by Victor Alexandrov
Mathematics · #math.MG #math.DG #msc:52C25 #msc:51B20 #msc:52B70 #msc:52B11 #msc:51M25
published as manuscripta math. 111 (2003) 3, 341-356. DOI 10.1007/s00229-003-0375-3 · 13 pages, 4 figures, LaTeX 2.09
arxiv created 2001/11/01 · arxiv updated 2009/11/30
Given a polyhedral surface, assume that it is prohibited to change the shape and size of any face but it is permissible to change the dihedral angles between the faces. A polyhedral surface is said to be flexible if it is possible to change its shape under the above restrictions. We prove that flexible polyhedral surfaces without boundary do exist in the Minkowski 3-space and each of them preserves the (inclosed) volume and the (total) mean curvature during a flex. To prove the latter result, we introduce the notion of the angle between two arbitrary non-null nonzero vectors in the Minkowski plane. The latter notion may be of some independent interest.