27 Mar
2009
27 Mar
'09
8 p.m.
On 3/28/09, Dan Asimov <dasimov@earthlink.net> wrote:
I accidentally (re-)discovered the circles of Villarceau c. 1992 when trying to foliate an open subset of 3-space by congruent circles. But in fact Villarceau discovered these in 1848. ... But this leaves unresolved infinitely many cases of k-spheres in n-space. First open case: Can congruent round 2-spheres foliate a non-empty open set in R^5 ???
What exactly is a "round sphere" in this context? I'd guess it's embedded topologically in the vanilla fashion --- but is metrically standard as well? WFL