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arXiv:math.MG/0111003v11Nov2001 Flexible polyhedra in the Minkowski 3-space
 

Summary: arXiv:math.MG/0111003v11Nov2001
Flexible polyhedra in the Minkowski 3-space
Victor Alexandrov
Sobolev Institute of Mathematics, Novosibirsk-90, 630090, Russia. E-mail:
alex@math.nsc.ru
Abstract
We prove that flexible polyhedra do exist in the Minkowski 3-space and each of them preserves
the (generalized) 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.
2000 Mathematics Subject Classification: 52C25, 51B20, 52B70, 52B11, 51M25
Key words: flexible polyhedron; Minkowski space; Minkowski plane; volume; total mean curvature;
angle
1 Introduction
Recall that the Minkowski n-space Rn
1 is the linear space which consists of all ordered n-tuples of reals
x = (x1, x2, . . . , xn) and is endowed with the following scalar product: (x, y) = x1y1 + x2y2 + . . . +
xn-1yn-1 - xnyn. The length |x| = (x, x) of a vector x is either a positive number or the product of a
positive number by the imaginary unity i, or zero (see, for example, [15]).
Let be a connected (n - 1)-dimensional simplicial complex which is a manifold. A continuous map

  

Source: Alexandrov, Victor - Sobolev Institute of Mathematics, Russian Academy of Sciences, Novosibirsk

 

Collections: Mathematics