Flexible polyhedra in the Minkowski 3space
Abstract
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 3space 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 nonnull nonzero vectors in the Minkowski plane. The latter notion may be of some independent interest.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 October 2001
 arXiv:
 arXiv:math/0111003
 Bibcode:
 2001math.....11003A
 Keywords:

 Mathematics  Metric Geometry;
 Mathematics  Differential Geometry;
 52C25 (Primary);
 51B20;
 52B70;
 52B11;
 51M25 (Secondary)
 EPrint:
 13 pages, 4 figures, LaTeX 2.09