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September 11th, 2016, 03:30 PM  #1 
Senior Member Joined: Apr 2014 From: zagreb, croatia Posts: 234 Thanks: 33 Math Focus: philosophy/found of math, metamath, logic, set/category/order/number theory, algebra, topology  Please suggest me a differential geometry book
Can someone please suggest me a good differential geometry book? I'm somewhat confused. There's so many of them. I have O'Neill, but found it not rigorous enough and he only works in 3d, as does Do Carmo. I obtained some knowledge on differentiable manifolds from 0th chapter of his other book, Riemannian geometry. But I much prefer Lee. But then again, there's also Kuhnel, and that I can actually understand, for Lee I'd have to read Massey and/or Boothby first. What should I do? Thanks in advance. Last edited by skipjack; September 12th, 2016 at 04:57 PM. 
September 12th, 2016, 02:36 PM  #2 
Senior Member Joined: Jun 2015 From: England Posts: 796 Thanks: 233 
Don't throw O'Neil away just yet. His book, after all, is called Elementary DG. But it does have the advantage of being modern. But it really depends where you want to go with this, O'Neil is a pure maths book in that it is about shapes of objects in multi dimensional space without regard to what the axes or the surfaces, curves etc mean. If you want to look at applications to say thermodynamics, relativity, quantum mechanics, fibre bundles, Hodge operators etc at a somewhat higher level then try Applied Differential Geometry W Burke Cambridge University Press If you want formalism without going back to Cartan or Guggenheim then try the MIT book Differential Geometry N Prakash McGrawHill 

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