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  Volume 10, Issue 1, Article 28
 
On a Problem for Isometric Mappings of $\mathbb{S}^n$ Posed by Th. M. Rassias
    Authors: Anup Biswas, Prosenjit Roy,  
    Keywords: $n-$sphere, isometry.  
    Date Received: 17/10/08  
    Date Accepted: 06/01/09  
    Subject Codes:

51K99

  
    Editors: Themistocles M. Rassias,  
 
    Abstract:

In this article we prove the problem on isometric mappings of $ mathbb{S}^{n} $ posed by Th. M. Rassias. We prove that any map $ f:mathbb{S}^{n}ightarrow mathbb{S}^{p},$ $ pgeq n>1$, preserving two angles $ heta $ and $ m heta $ ( $ m heta pi $) is an isometry. With the assumption of continuity we prove that any map $ f:mathbb{S}^{n}ightarrow mathbb{S}^{n}$ preserving an irrational angle is an isometry.

         
       
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