FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1995, VOLUME 1, NUMBER 1, PAGES 281-288

Quasi-conformal mappings of a surface generated by its isometric transformation, and bendings of the surface onto itself

I.Kh.Sabitov

It is proved that any surface S^* isometric to a given compact surface S and disposed sufficiently close to S generates a quasi-conformal mapping of S onto itself. On the base of this result it is proved that a compact surface admitting sliding bendings onto itself is topologically a sphere or a torus and its intrinsic metric is of rotation type.

All articles are published in Russian.

Location: http://mech.math.msu.su/~fpm/eng/95/951/95116.htm
Last modified: October 7, 1997.