34 citations · 125 across the 47 of their papers we have counts for
4 papers · 1 filter
Osculating curves: around the Tait-Kneser Theorem
E. Ghys, S. Tabachnikov, V. Timorin
The Tait-Kneser theorem states that the osculating circles of a plane curve with monotonic curvature are pairwise disjoint and nested. We discuss this theorem and a number of its v…
Maps That Take Lines to Circles, in Dimension 4
Vladlen Timorin
We list all analytic diffeomorphisms between an open subset of the 4-dimensional projective space and an open subset of the 4-dimensional sphere that take all line segments to arcs…
Kahler metrics whose geodesics are circles
Vladlen Timorin
We classify all Kahler metrics in an open subset of whose real geodesics are circles. All such metrics are equivalent (via complex projective transformations) to Fubini metri…
Rectification of circles and quaternions
Vladlen Timorin
Consider a bundle of circles passing through 0 in 4-dimensional space. It is said to be rectifiable if there is a germ of diffeomorphism at 0 that takes all circles from our bundle…