I think you are referring to differential geometry - right?

Know the story on how Gauss chose (wickedly!) this subject for Riemann to present as his doctoral thesis?

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- Aug 20th 2006, 07:09 AM #1

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- Aug 20th 2006, 09:23 AM #2

- Aug 20th 2006, 10:25 AM #3

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Originally Posted by**Rebesques**

Originally Posted by**Rebesques**

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Do you think I can follow it? I respect Riemann very much, but I do not know much about his work because unlike Gauss, Euler he primarily focused in only one area.

- Aug 20th 2006, 10:43 AM #4
Well, you can begin with the differential geometry of curves and surfaces. But note that it requires some calculus and differential equations, especially when you get into details. Believe me, it is rewarding. Plus, the formulas are really exquisite (and so really beautiful), check the Gauss-Bonnet formula.

To get into manifolds is a different matter. It requires some topology and some heavy calculus. But still, the results are striking!

Good luck and -above all- maintain your persistance.

- Aug 20th 2006, 10:48 AM #5

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Is it supposed to be some generalization of regions and surfaces?

(That formula was too advanced for me )

Originally Posted by**Rebesques**

This is mine 21th post!!!

- Aug 20th 2006, 11:06 AM #6Is it supposed to be some generalization of regions and surfaces?

That formula was too advanced for me

Let me see if i can find some link to a better treatment of the subject...

My guess it that in college such a course was optional and most poeple omitted it.

Well, in the special case they even exist, most people just avoid them - nothing wrong in that, it's a matter of personal gust.

- Aug 20th 2006, 12:30 PM #7
Here, PH, see if you find this link helpful.

http://people.hofstra.edu/faculty/St...f_geom/tc.html

- Aug 20th 2006, 01:13 PM #8

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- Aug 21st 2006, 04:09 PM #9