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I was wondering if anyone could recommend an introductory book for differential geometry. I am studying general relativity and need some help with this topic.

Thanks.

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- #1

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I was wondering if anyone could recommend an introductory book for differential geometry. I am studying general relativity and need some help with this topic.

Thanks.

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Landau

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Modern Differential Geometry for Physicists by Isham is a good one.

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dx

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"Applied Differential Geometry" by William Burke

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Fredrik

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I like Isham's book too. I think he covers some concepts, in particular the tangent space, even better than Lee. But it's not really an introduction to the differential geometry you need to understand GR. It's an introduction to the differential geometry you need to understand Yang-Mills theory. So he talks a lot about Lie groups and fiber bundles, which you don't need right now, and doesn't say much about geodesics and curvature.

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Isham's book was a little to advanced. I was able to find one though to suit my needs. It doesn't look like it is too popular but its called "Introduction To Differential Geometry and Reimannian Geometry By: Erwin Kreyszig"

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Fredrik

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I very much doubt that, but as I said, it's going in the wrong direction for you. It's preparing the reader for Yang-Mills theory, not GR.Isham's book was a little to advanced.

His functional analysis book is very popular, so he seems to know how to write good books. I'm sure it's fine, but it's hard to beat Lee. Hm, there's also a book by a guy named Manfredo Perdigão do Carmo that's getting good reviews at Amazon.I was able to find one though to suit my needs. It doesn't look like it is too popular but its called "Introduction To Differential Geometry and Reimannian Geometry By: Erwin Kreyszig"

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Landau

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It does require more mathematical prequisites than most physics students have.I very much doubt that

His FA book is ok. But if we're talking about https://www.amazon.com/dp/0486667219/?tag=pfamazon01-20&tag=pfamazon01-20 (perhaps an expanded version including Riemannian Geometry?), I have to warn OP: this is prettyHis functional analysis book is very popular, so he seems to know how to write good books. I'm sure it's fine,

Lee is pretty good in my opinion, but of course it's not the only one. These all have their merits:but it's hard to beat Lee. Hm, there's also a book by a guy named Manfredo Perdigão do Carmo that's getting good reviews at Amazon.

Tu - An Introduction to Manifolds

Spivak - A comprehensive introduction to differential geometry Vol I

Darling - Differential Forms and Connections

Lang - Introduction to Differentiable Manifolds

Conlon - Differentiable Manifolds

Barden, Thomas - An Introduction to Differential Manifolds

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Fredrik

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Don't they all?It does require more mathematical prequisites than most physics students have.

Ughh...that sucks. I want everything to be as coordinate-independent as possible. I retract my "I'm sure it's fine" comment.I have to warn OP: this is prettyold-fashioned! Everything is done in local coordinates, and mostly in three dimensions.

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