activity
20002004
most citedMaps That Take Lines to Circles, in Dimension 4

4 citations · 8 across the 4 of their papers we have counts for

collaborators

7 papers

math.NT20041 cited

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…

math.DG20034 cited

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…

math.MG20023 cited

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…

math.MG2002

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…

math.DG2001

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…

math.DG2001

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…