Most efficient backgrounder on differential geometry ?

[lalbatros]

I am used to classical tensor notations. I am doing theoretical physics during my hobby time, engineering for a living.
Often I get lost with differential forms notations and even I don't recognize easily the concepts. I don't have the patience to re-read the full text of the wonderful 'Gravitation' book by Wheeler.

Could some of you indicate me a very short book going fast to the point.

Thanks for your understanding !

 

[mathwonk]

try the article by flanders in this volume: and the price is right. but i suggest you go back and read wheeler afterwards. what is so important, if you really want to understand the topic, to keep you from reading the book where you know perfectly well it is explained excellently?

Studies in Global Differential Geometry
Series: Studies in Mathematics

Editor: S.S. Chern


This is a most useful collection of papers for theoretical physicists. Flander's article on differential forms gives an excellent introduction to the subject. The other articles are more advanced, but they are all interesting to physicists who are now in daily contact with ideas and facts in global geometry.-C.N. Yang, Nobel Laureate

320 pp., Hardbound, 1989
ISBN 0-88385-129-6
Sale Price: $7.95
Catalog Number: MAS-27/W

http://www.maa.org/pubs/books/mas27.html

 

[lalbatros]

This one is available on the www:

http://books.pdox.net/Math/Differential%20Geometry%20in%20Physics.pdf (Gabriel Lugo)​

It goes fast to the point. He makes a few remarks that help demystify the notations.

 

[quetzalcoatl9]

i have over a dozen books on the subject, and i have found the best to be "The Geometry of Physics" by Frankel.

another book "Tensor Analysis on Manifolds" by Bishop is very good (it is a classic), but somewhat cryptic at times.

for a very easy intro to differential forms, "Differential Forms" by Weintraube is great. for a more sophisticated treatment of the subject, the book "Differential Forms and Connections" by Darling is good.

I would recommend staying away from the Dover books...yes, they are cheap, but I found them difficult to follow. Good for reference, but if you are just learning the stuff I would get some better texts.

If you are learning it by yourself, it is good to surround yourself with different texts since if you get stuck, you can just switch books and see if the same thing is explained differently.