Maths required to start differential geometry

[dyn]

I have a Physics background and have done the relevant maths ie. calculus , linear algebra , vector calculus and differential equations. Do i need any "extra maths" before starting a course in differential geometry ? Any recommendations for a book on the subject that would suit a Physicist ?
Thanks

 

[lurflurf]

It depends what you mean by all those words. Some courses are pitched at a level just past calculus, you would have ideal preparation for such a course. Some courses are pitched at a higher level, for which you would want to know more calculus, some topology, some algebra (beyond linear algebra), and know a little bit about manifolds. Does "physics background" mean you have done much with general relativity, differential forms, symplectic geometry, or tensor calculus? As you probably know there is some overlap between those areas and differential geometry.

A book that might be of some interest is Curvature in Mathematics and Physics by Shlomo Sternberg though it is not easy

A problem when learning differential geometry is that many books are too easy, many books are too hard, and many books are about parts of differential geometry that are not relevant to your goals. It is hard to find one that is just right sometimes.

 

[dyn]

Thanks. I have done some General Relativity but no topology or analysis or manifolds. I need a book that starts from the absolute basics.

 

[Matterwave]

For a physicist, I recommend Bernard Schutz Geometrical Methods of Mathematical Physics. He gives a quick overview of the math that you need at the beginning of the book. It's easy to follow.

 

[George Jones]

Thanks. I have done some General Relativity but no topology or analysis or manifolds. I need a book that starts from the absolute basics.

Are you interested in general relativity, or for elementary particle gauge field theory, or for both.

 

[dextercioby]

Thanks. I have done some General Relativity but no topology or analysis or manifolds. I need a book that starts from the absolute basics.

Doing GR without differential geometry, hmm... I can only think of 3 books (Feynman, Weinberg, Dirac), since differential geometry became what we know today, i.e. after 1950.

Schutz is a good option, Takahara is a good option.