differential geometry / working knowledge

On Aug 4, 6:46 am, craigt wrote:
I know someone will rip me a new one if I ask this but:

Just wondering where one can look for a working knowledge of diff. geom., I want to be able to look at inequalities and so will need an understanding of
L^p and Sobolev spaces over manifolds and also an understanding of some PDEs on manifolds.
I at least don't want to be scared to write down the Laplace-Belltrami operator (or whatever you call it)

I want to avoid all the usual stuff... you know like, dare I say it, charts, atlases ...

In the same sense I think someone could have a fairly good understanding of the Lebesgue and Sobolev spaces on an open set in R^n without having a deep understanding of measure theory.

thanks

name withheld

Here are some well readable books of differential
geometry and almost all present mathematics
(encyclopaedia), if I mention only some:

O'Neill,B., 1966.
Elementary Differential Geometry.
Academic Press, Inc., New York, United States of America,
411 pages.

Lipschutz,M.M, 1969.
Theory and Problems of Differential Geometry.
Schaum's Outline Series, McGraw-Hill Book Company,
New York, United States of America, 269 pages.

Encyclopaedia of Mathematics, 1995.
Volumes 1-10, Index volume (volume 10) 1994,
Supplement I, 1997,
Reidel, Kluver Academic Puiblishers, Science
and Technology Divisions, Netherlands.
(Other name of the series: Vinogradov,L.M.(Editor), 1995.
Soviet Mathematical Encyclopaedia. "Soviet Encyclopaedia"
Publishing House.)

Folland Gerald, B., 1995.
Introduction to partial differential equations.
2. nd edition, Princeton University Press, Princeton,
New Jersey. Printed in the United States oof America.
323 pages.

I hope I could help.

Best Regards,

Hannu Poropudas