On Conservative Mapping of Aleksandrov Problem
Received:March 25, 2005  Revised:July 05, 2006
Key Word: distance-$\rho$ preserving mapping   strongly distance-$\rho$ preserving mapping   isometry mapping   Aleksandrov problem.
Fund ProjectL:the National Natural Science Foundation of China (10571090).
 Author Name Affiliation REN Wei-yun School of Science, Tianjin University, Tianjian 300072, China
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Let $E$ and $F$ be real Hilbert spaces, and $f:E\rightarrow F$ be a mapping. This paper shows that $f$ is an affine isometry if $f$ preserves distance $a$ and $b$ (where $a, b$ are two positive real numbers) and satisfies some additional conditions, and hence partly answers the Aleksandrov problem.