# Intro to differential geometry with worked examples

1. Sep 18, 2014

### dyn

Hi. I am looking for the most basic intro to differential geometry with plenty of worked examples. I want it to cover the following - differential forms , pull-backs , manifolds , tensors , metrics , Lie derivatives and groups and killing vectors. Problems with solutions would also be good as I am self-studying. I already have the book " Geometrical methods of mathematical physics" by Schutz. Thanks.

2. Sep 21, 2014

### George Jones

Staff Emeritus
Maybe Fecko:

Last edited by a moderator: May 6, 2017
3. Sep 23, 2014

### dextercioby

If you think Fecko is too difficult, perhaps Nakahara's (2nd edition) could serve as an alternative. The examples are from physics.

4. Oct 6, 2014

### NumericalFEA

Last edited by a moderator: May 7, 2017
5. Oct 16, 2014

### Daverz

Last edited by a moderator: May 7, 2017
6. Oct 16, 2014

### SteamKing

Staff Emeritus
You can always try the Schaum's Outline of Differential Geometry:

https://www.amazon.com/Schaums-Outline-Differential-Geometry/dp/0070379858

This series contains worked examples and plenty of practice problems. IDK if it covers all the topics on your list, but it will get you started with the basics.

Last edited by a moderator: May 7, 2017
7. Oct 16, 2014

### SteamKing

Staff Emeritus
Last edited by a moderator: May 7, 2017
8. Oct 17, 2014

### dyn

Is tensor calculus part of differential geometry or are they separate subjects ? Is General Relativity taught in 2 different ways ; one using tensors and one using differential forms or are they both combined in GR ?

9. Oct 17, 2014

### dextercioby

Tensor calculus is a part of differential geometry. GR is taught using tensors at the standard level. Using differential forms (Cartan calculus) is a fancy but useful way to write it, expecially when one thinks of GR's extensions: PGT, EC, SUGRA, etc.

10. Oct 17, 2014

### SteamKing

Staff Emeritus
Tensors can show up in other areas of math and physics besides diff. geometry. One place I seem to stumble over them occasionally is in finding the principal axes of a general 3-D body. There are other applications in mechanics, involving stress analysis.

A lot of geometry has been formulated these days using matrix methods, to facilitate doing numerical calculations with computers, and it seems you run into tensors as a consequence of this also.