Timeline for homogeneous surface in $\mathbb{R}^4$

7 events

when toggle format	what		by	license	comment
Jul 25, 2017 at 15:59	comment	added	Robert Bryant		@IgorRivin: In fact, though, the homogeneous hypersurface case in Euclidean space is not very interesting: It's a classical fact that a homogeneous hypersurface in $\mathbb{E}^{n+1}$ is an orthogonal product of the form $S^p\times \mathbb{E}^{n-p}$ for some $0\le p\le n$. (This is far from the case in positive curvature, of course, i.e., in $S^{n+1}$, as there are quite a few interesting homogeneous hypersurfaces in that case. See the extensive work on isoparametric hypersurfaces, for example.)
Jul 25, 2017 at 10:20	comment	added	Paul		Yes, I forget it in my question.
Jul 24, 2017 at 18:27	comment	added	Igor Rivin		Hypersurfaces seem more interesting...
Jul 24, 2017 at 18:15	comment	added	Wlodek Kuperberg		Also, it would be interesting to know all connected homogeneous curves in ${\mathbb R}^4$, curves and surfaces in ${\mathbb R}^5$, and so on.
Jul 24, 2017 at 18:04	history	edited	Wlodek Kuperberg	CC BY-SA 3.0	one sentence added
Jul 24, 2017 at 18:01	comment	added	Ben McKay		Also called the Clifford torus.
Jul 24, 2017 at 17:56	history	answered	Wlodek Kuperberg	CC BY-SA 3.0