Extens\~oes de isometrias da esfera de dimens\~ao n

TL;DR

This paper discusses extensions of isometries on the n-dimensional sphere, but was withdrawn for integration into a broader work on applications in inner product spaces.

Contribution

It introduces new extensions of isometries on spheres within vector spaces with inner products, enhancing understanding of geometric transformations.

Findings

Extended isometries characterized for n-dimensional spheres

New methods for applying isometries in inner product spaces

Theoretical framework for sphere transformations

Abstract

This article was withdrawn by the author to be incorporated into the paper "Extens\~ao de aplica\c{c}\~oes na esfera de um espa\c{c}o vetorial com produto interno" (arXiv:1109.2866).