10 citations · 33 across the 18 of their papers we have counts for
18 papers · 1 filter
Hexagonal 3-webs of circles with polar twisted cubic
Sergey I. Agafonov
The paper describes and classifies hexagonal circular 3-webs on unit sphere such that the polar points of the web circles lie on a twisted cubic, thus completing classification of…
Integrable geodesic flows with simultaneously diagonalisable quadratic integrals
Sergey I. Agafonov, Vladimir S. Matveev
We show that if functionally independent commutative quadratic in momenta integrals for the geodesic flow of a Riemannian or pseudo-Riemannian metric on an -dimensional mani…
Integrable geodesic flow in 3D and webs of maximal rank
Sergey I. Agafonov
We characterize geodesic flows, admitting two commuting quadratic integrals with common principal directions, in terms of the geodesic 4-webs such that the tangents to the web leav…
Fractional-linear integrals of geodesic flows on surfaces and Nakai's geodesic 4-webs
Sergey I. Agafonov, Thaís G. P. Alves
We prove that if the geodesic flow on a surface has an integral, fractional-linear in momenta, then the dimension of the space of such integrals is either 3 or 5, the latter case c…
Hexagonal Circular 3-Webs with Reducible Polar Curves of Degree Three
Sergey I. Agafonov
The paper reports the progress with the classical problem, posed by Blaschke and Bol in 1938. We present new examples and new classifications of natural classes of hexagonal circul…
Darboux integrability for diagonal systems of hydrodynamic type
Sergey I. Agafonov
We prove that 1) diagonal systems of hydrodynamic type are Darboux integrable if and only if the corresponding systems for commuting flows are Darboux integrable, 2) systems for co…
Quadratic integrals of geodesic flow, webs, and integrable billiards
Sergey I. Agafonov
We present a geometric interpretation of integrability of geodesic flow by quadratic integrals in terms of the web theory and construct integrable billiards on surfaces admitting s…
Confocal conics and 4-webs of maximal rank
Sergey I. Agafonov
Confocal conics form an orthogonal net. Supplementing this net with one of the following: 1) the net of Cartesian coordinate lines aligned along the principal axes of conics, 2) th…
Duality for systems of conservation laws
Sergey I. Agafonov
For one-dimensional systems of conservation laws admitting two additional conservation laws we assign a ruled surface of codimension two in projective space. We call two such syste…
Hexagonal geodesic 3-webs
Sergey I. Agafonov
We prove that a surface carries a hexagonal 3-web of geodesics if and only if the geodesic flow on the surface admits a cubic first integral and show that the system of partial dif…
Projective invariants of linear 3-webs and Gronwall's Conjecture
Sergey I. Agafonov
We present a projectively invariant description of planar linear 3-webs. For a non-hexagonal 3-web, we introduce family of projective torsion-free Cartan connections, the web leave…
Quasilinear systems with linearizable characteristic webs
S. I. Agafonov, E. V. Ferapontov, V. S. Novikov
We classify quasilinear systems in Riemann invariants whose characteristic webs are linearizable on every solution. Although the linearizability of an individual web is a rather no…
Note on generic singularities of planar flat 3-webs
Sergey I. Agafonov
We propose a definition of genericity for singular flat planar 3-webs formed by integral curves of implicit ODEs and give a classification of generic singularities of such webs.
Gronwall's conjecture for 3-webs with infinitesimal symmetries
Sergey I. Agafonov
We study non-flat planar 3-webs with infinitesimal symmetries. Using multi-dimensional Schwarzian derivative we give a criterion for linearization of such webs and present a projec…
Flat 3-webs via semi-simple Frobenius 3-folds
Sergey I. Agafonov
We construct flat 3-webs via semi-simple geometric Frobenius manifolds of dimension three and give geometric interpretation of the Chern connection of the web. These webs turned ou…
Local classification of singular hexagonal 3-webs with holomorphic Chern connection and infinitesimal symmetries
Sergey Agafonov
We provide a complete classification of hexagonal singular 3-web germs in the complex plane, satisfying the following two conditions: 1) the Chern connection remains holomorphic at…
On implicit ODEs with hexagonal web of solutions
S. I. Agafonov
Solutions of an implicit ODE form a web. Already for cubic ODEs the 3-web of solutions has a nontrivial local invariant, namely the curvature form. Thus any local classification of…
Systems of conservation laws of Temple class, equations of associativity and linear congruences in projective space
S. I. Agafonov, E. V. Ferapontov
We propose a geometric correspondence between (a) linearly degenerate systems of conservation laws with rectilinear rarefaction curves and (b) congruences of lines in projective sp…