Zobrazeno 1 - 10
of 74
pro vyhledávání: '"Agafonov Sergey"'
We show that if $n$ functionally independent commutative quadratic in momenta integrals for the geodesic flow of a Riemannian or pseudo-Riemannian metric on an $n$-dimensional manifold are simultaneously diagonalisable at the tangent space to every p
Externí odkaz:
http://arxiv.org/abs/2403.14319
Autor:
Agafonov, Sergey I.
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 leaves are common zero directions of the integrals. We prove that, under s
Externí odkaz:
http://arxiv.org/abs/2403.01459
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 corresponding to constant gaussian curvature. We give also a geometric
Externí odkaz:
http://arxiv.org/abs/2306.17540
Autor:
Agafonov, Sergey I.
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 circular 3-webs. The main results is the classification of hexagonal circula
Externí odkaz:
http://arxiv.org/abs/2306.11707
Autor:
Agafonov, Sergey I.
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 commuting flows are Darboux integrable if and only if the Laplace transf
Externí odkaz:
http://arxiv.org/abs/2105.14496
Autor:
Agafonov, Sergey I.
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 such integrals.
Comment: 10 pages
Comment: 10 pages
Externí odkaz:
http://arxiv.org/abs/2004.12374
Autor:
Agafonov, Sergey I.
Publikováno v:
In Differential Geometry and its Applications December 2023 91
Autor:
Agafonov, Sergey I.
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) the net of Apollonian pencils of circles whose foci coincide with the fo
Externí odkaz:
http://arxiv.org/abs/1912.01817
Autor:
Agafonov, Sergey I.
Publikováno v:
Lett. Math. Phys. 2019
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 systems dual if the corresponding ruled surfaces are dual. We show that a H
Externí odkaz:
http://arxiv.org/abs/1908.00585
Autor:
Agafonov, Sergey I.
Publikováno v:
Int. Math. Res. Not. IMRN, 2019
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 differential equations, governing metrics on such surfaces, is integrable
Externí odkaz:
http://arxiv.org/abs/1806.03072