Elliptic geometry in 3 dimensions

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I'm interested in elliptic space from an intrinsic point of view(manifold pov) rather than the models based in Euclidean embeddings.
Would it be correct to say that the isometry group of this geometry is isomorphic to SU(2), i.e.:versors or unit quaternions?
 
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Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
 

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