Elliptic geometry in 3 dimensions

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Elliptic geometry in three dimensions is examined from an intrinsic manifold perspective, focusing on its unique properties rather than Euclidean models. The discussion raises the question of whether the isometry group of this geometry is isomorphic to SU(2), which relates to versors or unit quaternions. There is a request for additional insights or conclusions on the topic, indicating a desire for deeper exploration. The lack of responses suggests a need for further clarification or rewording of the original inquiry. Overall, the conversation seeks to deepen understanding of elliptic geometry's intrinsic characteristics.
TrickyDicky
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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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