Extens\~ao de aplica\c{c}\~oes na esfera de um espa\c{c}o vetorial com   produto interno
  Being E a vector space with inner product and S the sphere of E, will be given a demonstration that every application of the sphere S itself it such that preserve inner product is the restriction of a linear isometry in E. 
J. Edson Sampaio
math.FA math.DG