Talk:Gauss map

The range of the Gauss map

I believe the range of the Gauss map is the unit sphere, not the unit circle: the normal vector is a three dimensional vector. I did an edition, but please check whether it's correct. --Anša (talk) 19:16, 5 September 2009 (UTC)

S² is the unit sphere and so it was correct previously.

Grassmannian

The Grassmannian page does talk about unoriented k-subspaces, so the notation here isn't yet consistent with that there.

Charles Matthews 13:01, 27 Nov 2003 (UTC)

Thanks Charles for reminding me of that. I have changed grassmannian to oriented grassmannian, though I am not sure of the name. It seems that in the litterature, both are called grassmannian, with definition depending on context. I wonder whether we should expand on that notion in Grassmannian ...

Good editing work too: it does look clearer that way (and the english is better, I guess).

By the way, since you seem to have a lot more experience with Wikipedia, is there some kind of hierarchy (sections, chapters and what not) where one should (could ?) register these pages ? Like any page on math should belong to the math "section", and so on.

Pascalromon 21:45, 27 Nov 2003 (UTC)

On orientations: the Grassmannian page should point out that the orthogonal group acts transitively also on oriented k-subspaces, and so on: the distinction should be clarified there.

As for lists/hierarchy, this should be linked from list of mathematical topics (G-I) (and is already); and also from list of differential geometry topics. I would do this in time - I tend to wait until I have a few to add, though.

Charles Matthews 22:08, 27 Nov 2003 (UTC)

Generalizations

I think the generalization given here should be limited to Euclidean n-space, the generalization for manifold formally works, but it does not seems to be used at all, so if it is useless for me it is defenately useless for reader who wants to know what is Gauss map.

Tosha 04:32, 5 Mar 2004 (UTC)

radial of a curve

given a plane curve, take all the radiuses of tangent circles and move them to the origin. The end points forms what's called the radial curve of the given curve. Xah Lee 01:49, 2005 May 1 (UTC)

Thanks for mentioning. A nice article on that (and a link from this article) would not hurt. Oleg Alexandrov 02:13, 1 May 2005 (UTC)

Degree of a Gauss map

The degree of a Gauss map is mentioned in this article and elsewhere, for example in Smale's paradox, but is not defined here. Can this be added? — Cheers, Steelpillow (Talk) 08:17, 4 September 2010 (UTC)