arXiv research

This paper is devoted to study the Lie algebra of linear symmetries of a homogenous 2nd order ODE, by the method of Kushner, Lychagin and Robstov.

Method finds MAEs on contactified para-Kähler manifolds.

In this lecture delivered at the Integrable and Quantum Field Theory at Peyresq sixth meeting, we review the Lychagin's Monge-Ampere operators theory and exhibit the link it establishes between the classical problem of local equivalence for non linear partial differential equations and the problem of integrability of s…

A differential 1-form $α$ on a manifold of odd dimension $2n+1$, which satisfies the contact condition $α\wedge (dα)^n \neq 0$ almost everywhere, but which vanishes at a point $O$, i.e. $α(O) = 0$, is called a \textit{singular contact form} at $O$. The aim of this paper is to study local normal forms (formal, analytic …

In the article "On the linearizability of 3-webs" (Nonlinear analysis 47, (2001) pp.2643-2654), published in 2001, we studied the linearizability problem for 3-webs on a 2-dimensional manifold. Four years after the publication of our article, V.V.Goldberg and V.V.Lychagin in the paper "On linearization of planar three-…

We define a nondegenerate Monge-Ampère structure on a 6-dimensional manifold as a pair $(Ω,ω)$, such that $Ω$ is a symplectic form and $ω$ is a 3-differential form which satisfies $ω\wedgeΩ=0$ and which is nondegenerate in the sense of Hitchin. We associate with such a pair a generalized almost (pseudo) Calabi-Yau stru…

We define a non-degenerated Monge-Ampere structure on a 6-manifold associated with a Monge-Ampere equation as a couple (Ω,ω), such that Ωis a symplectic form and ωis a 3-differential form which satisfies ω\wedgeΩ=0 and which is non-degenerated in the sense of Hitchin. We associate with such a couple an almost (pseudo) …

The paper clarifies thermodynamics on non-compact symmetric spaces using Kähler geometry.