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on September 4, 2012
It is one of the less pretentious books on this subject (although a bit expensive I think); and yet, I found it quite a good one. Would give it 4.5 stars, the minus is due to a vague feeling that it could be better, maybe the style, too dry, not enough of a "literature", and few typos in equations (very few) that can be tracked by the careful reader (and it is hard to blame the author, since the math is quite dense). Otherwise, a meticulous review of tensors, a stand alone reference, from basic introduction to advanced material such as the concept of Killing vector field. A very detailed explanation and derivations, for example, one of the best source for derivation of the equations of geodesy I've encountered so far, using few approaches, and a nice proof for the possibility of a local vanishing of the Christoffel symbols (the principle of equivalence in general relativity). In general, the book is general relativity oriented (the various metric of the examples are usually taken from GR), and I suspect that it was inspired to some degree by Weinberg's Gravitation and Cosmology. Again, the book is very detailed and you can find many tensorial relations which are hard to find in other places, all explicitly derived, many examples and solved exercises. Somehow, this book reminds me another good book written also in India: Differential Geometry of Manifolds by De and Shaikh, more on coordinate free approach, can be a good complement to this book.
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