4 citations · 8 across the 4 of their papers we have counts for
7 papers
On binary quadratic forms with semigroup property
Francesca Aicardi, Vladlen Timorin
A quadratic form f is said to have semigroup property if its values at points of the integer lattice form a semigroup under multiplication. A problem of V. Arnold is to describe al…
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…
Circles and Quadratic Maps Between Spheres
Vladlen Timorin
Consider an analytic map of a neighborhood of 0 in a vector space to a Euclidean space. Suppose that this map takes all germs of lines passing through 0 to germs of circles. Such a…
Circles and Clifford Algebras
Vladlen Timorin
Consider a smooth map from a neighborhood of the origin in a real vector space to a neighborhood of the origin in a Euclidean space. Suppose that this map takes all germs of lines…
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…