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Can someone please point me to introductory resources about the geometry of Anti DeSitter Space ? What are some examples of other spaces used in theoretical physics ?.I'm learning Differential Geometry right now , I want to apply what I learn on simple spaces of importance in theoretical physics. Like , I want to investigate the nature of these spaces , calculate their metrics , curvature and other things.

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Moschellas's "deSitter and Anti deSitter Sightseeing Tour" is pretty good available here –  twistor59 May 22 '12 at 18:19
    
Related: physics.stackexchange.com/q/17093/2451 –  Qmechanic May 22 '12 at 18:22
    
Thanks you , guys . Is it a good idea to try to apply things that I learn in differential geometry on spaces like Ads and others? –  EGY May 22 '12 at 19:25
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@EGY: It's necessary--- but AdS spaces are symmetric, so if you don't do calculations that take the symmetry into account, you are doing too much work. –  Ron Maimon May 23 '12 at 5:28
    
Thanks , Ron . I know that I have to take symmetry into account . I have one more seemingly unrelated question , What are the topics in string theory that can be understood with only a mathematical background in topology,algebraic topology and analysis on manifolds? I have studied only very introductory topics in quantum field theory (Only the first four chapters in peskin) –  EGY May 23 '12 at 10:08

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