Talk:Differential geometry of surfaces

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Mathematics rating:	B Class	High Priority	Field: Geometry
Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments. Please add to or update the comments to suggest improvements to the article. The lead needs some work, and there could be more on extrinsic curvature, but this is comfortably B-class. Geometry guy 12:12, 13 April 2008 (UTC)

[edit] Introduction

I have restored introductory material describing the scope of the subject. It's good to see the forest before embarking on the detailed study of the trees … Arcfrk (talk) 22:38, 3 February 2008 (UTC)

Auguri, U r doing an excellent travail!--kiddo (talk) 17:52, 12 February 2008 (UTC)

[edit] normal coordinates change ?

The following sentence :

== Taking a coordinate change from normal coordinates at p to normal coordinates at a nearby point q, yields the Sturm-Liouville equation satisfied by H(r,θ) = G(r,θ)½, discovered by Gauss and later generalised by Jacobi, Hrr = – K H. The Jacobian of this coordinate change at q is equal to Hr ==

is not clear. What is the link between a normal coordinate changes at p to q, and the equation Hrr = – K H. ? Why Hr is the Jacobian of this coordinate change ? Thank you for your explanations. 139.124.7.126 (talk) 17:06, 26 March 2008 (UTC)

This classical computation is discussed for example in Berger's book. I'll give you a detailed explanation myslef, if I have time. Mathsci (talk) 13:50, 18 April 2008 (UTC)

[edit] Opener

Why would we have the opener sentence contrast with another subject, and moreover bad mouth it. Seems to be a shame, for there is much beauty in the differential theory of curves as well. Oded (talk) 06:16, 7 April 2008 (UTC)

I tend to agree with this comment. There are many kinds of questions that can be fruitfully studied in the curve situation that is different than the surface case. This is not a weakness but a strength. For example, curvature bounds and knot energies are related to knot type and that seems to be to be under the jurisdiction of "differential geometry of curves". I will remove that sentence for now, unless someone objects. --C S (talk) 15:43, 17 April 2008 (UTC)

Actually, it seems it would take a little work to remove the sentence, as it is so entangled in the lede. I will come look at it later. --C S (talk) 15:45, 17 April 2008 (UTC)

I completely agree. I have already said elsewhere that I do not like the lede, which was written by User:Arcfrk after he excised the main text, written almost wholly by me, from Surfaces. I also do not understand why he included the second paragraph, which has no relation to the contents of the article. Mathsci (talk) 13:47, 18 April 2008 (UTC)

I modified the lede accordingly. Oded (talk) 15:03, 18 April 2008 (UTC)

The first paragraph is very good now. (BTW nice to have you as a fellow WP editor!) Mathsci (talk) 15:44, 18 April 2008 (UTC)

thanks. Do I know you? Oded (talk) 16:18, 18 April 2008 (UTC)

Probably not. I was at MSRI during your "hot topic" week and have research interests in CFT, so I was very pleasantly surprised to see you here :) Mathsci (talk) 19:23, 18 April 2008 (UTC)

Actually, this should still be improved. The first sentence adopts the intrinsic viewpoint, while the second is explicitly assuming an embedding of the surface in Euclidean space. Oded (talk) 17:16, 18 April 2008 (UTC)

I tried to fix this. Hope it is better now.