Talk:Riemannian manifold
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I've come to terms with the fact that I will never understand this.
- You know, the article is much too short. It could stand to have many examples and explanatory sentences added. Perhaps you could help us decide how best to improve it, with focused questions. at what point does the exposition lose you? if you ask for more, you might receive it... - Lethe
- I added a paragraph to the article. I should probably look it over again tomorrow to make sure it's coherent, but I want to make the basic idea of a Riemannian manifold transparent; an inner product gives you a notion of length on a vector space, and a Riemannian metric gives you a notion of length on a smooth manifold by defining an inner product on each tangent space, pointwise, in a smooth way. to pass from a notion of length of a tangent vector to length of a curve on the manifold, all you have to do is integrate. There is a lot more you can do with Riemannian geometry, but if you can grasp that starting notion, then the rest should fall into place. I guess what I'm saying is, if you think the article is incomprehensible, you may be right. Asking for clarification might be a good idea.... Lethe
-- I think my new paragraph here kinda sticks out like a sore thumb. I don't like it, and perhaps it belongs in a different article (differential geometry, perhaps?) I'm looking for feedback, i guess. - Lethe 00:17, Jul 17, 2004 (UTC)