A. D. Alexandrov's Problem for CAT(0)-Spaces |
| |
Authors: | P D Andreev |
| |
Institution: | (1) Pomor State University, Arkhangel'sk, Russia |
| |
Abstract: | We solve the well-known problem by A. D. Alexandrov for nonpositively curved spaces. Let X be a geodesically complete locally compact space nonpositively curved in the sense of Alexandrov and connected at infinity. The main theorem reads as follows: Each bijection f : X → X such that f and the inverse f ?1 of f preserve distance 1 is an isometry of X. |
| |
Keywords: | Alexandrov's problem nonpositively curved space isometry |
本文献已被 SpringerLink 等数据库收录! |