Book on diff. geometry, tensors, wedge product forms etc.

[guguma]

Hi all,

I am taking this math methods course in grad school, and in the lectures we stormed through differential geometry. My geometry is already horrible, I find it hard to understand all these forms, fields, tensors, wedge products etc...

I would be glad if you could suggest some books for me to read about these. I would be glad to find one which does not go into immense details (i looked at some pure math books on geometry but my brain short circuited), but somehow covers all these stuff. I would also prefer if it had pictures in it. I am serious, my geometry is horrible and pictures make it much easier to understand them. I know that the book you are wishing for never exists but anything close to it would do.


Thanks in advance.

 

[dx]

For a very elementary but extremely clear exposition of one-forms, tangent vectors and tensors, try chapter 2 of "Spacetime, Geometry, Cosmology" by William Burke (this one has lots and lots of pictures). For a more sophisticated account, but still not going into too much detail, try "Gauge Fields, Knots and Gravity" By John Baez and Javier Muniain. Both of these are mainly physics books, so they have lots of applications of the formalism, which is always a good thing.

 

[^_^physicist]

Quick answer: Lovelock


Long Answer:
The author,, Lovelock, published a text years ago entitled something along the lines of "tensors, differential forms, and variational principles." Its in print currently by Dover. Short, sweet, and to the point for most of differential geometry.

If you want a more "hard-core text"

Modern Geometry- Methods and Applications by B. A. Dubrovin is a great series, though you will really only need part 1. Not quite as short, and somewhat painful at times. But overall very good.

 

[mathwonk]

for wedge products of forms and the associated geometry, the book by dave bachman, read communally here a while back, seemed excellent. (At the time, in my usual picky way, I criticized some professional level niceties, which will not bother a student.)