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pro vyhledávání: '"Moreno, Giovanni"'
We develop a method for describing invariant Monge-Amp\`ere equations in the sense of V. Lychagin and T. Morimoto (MAE) on a homogeneous contact manifold $N$ of a semisimple Lie group $G$, which is the contactification of the homogeneous symplectic m
Externí odkaz:
http://arxiv.org/abs/2402.08315
In this paper we study $3^{\mathrm{rd}}$ order (system of) PDEs in two independent variables $x,y$ and one unknown function $u$ that are invariant with respect to the group of affine transformation $\mathrm{Aff}(3)$ of $\mathbb{R}^3=\{(x,y,u)\}$. Aft
Externí odkaz:
http://arxiv.org/abs/2202.09894
For any second-order scalar PDE $\mathcal{E}$ in one unknown function, that we interpret as a hypersurface of a second-order jet space $J^2$, we construct, by means of the characteristics of $\mathcal{E}$, a sub-bundle of the contact distribution of
Externí odkaz:
http://arxiv.org/abs/2105.06675
Let $M = G/H$ be an $(n+1)$-dimensional homogeneous manifold and $J^k(n,M)=:J^k$ be the manifold of $k$-jets of hypersurfaces of $M$. The Lie group $G$ acts naturally on each $J^k$. A $G$-invariant PDE of order $k$ for hypersurfaces of $M$ (i.e., wit
Externí odkaz:
http://arxiv.org/abs/2004.04021
In [Alekseevsky, Gutt, Manno, Moreno: "A general method to construct invariant PDEs on homogeneous manifolds", Communications in Contemporary Mathematics (2021)] the authors have developed a method for constructing $G$-invariant PDEs imposed on hyper
Externí odkaz:
http://arxiv.org/abs/1907.06283
Akademický článek
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Complex contact manifolds, varieties of minimal rational tangents, and exterior differential systems
Autor:
Buczyński, Jarosław, Moreno, Giovanni
Publikováno v:
Banach Center Publications 117 (2019), 145-176
Complex contact manifolds arise naturally in differential geometry, algebraic geometry and exterior differential systems. Their classification would answer an important question about holonomy groups. The geometry of such manifold $X$ is governed by
Externí odkaz:
http://arxiv.org/abs/1805.08548
Publikováno v:
Banach Center Publications 117 (2019), 9-44
This paper contains a thorough introduction to the basic geometric properties of the manifold of Lagrangian subspaces of a linear symplectic space, known as the Lagrangian Grassmannian. It also reviews the important relationship between hypersurfaces
Externí odkaz:
http://arxiv.org/abs/1805.04294
In this paper we review a geometric approach to PDEs. We mainly focus on scalar PDEs in n independent variables and one dependent variable of order one and two, by insisting on the underlying (2n+1)-dimensional contact manifold and the so-called Lagr
Externí odkaz:
http://arxiv.org/abs/1708.02718
Autor:
Moreno, Giovanni, Stypa, Monika Ewa
Publikováno v:
Communications in Mathematics 24 (2016) 153-171
If a variational problem comes with no boundary conditions prescribed beforehand, and yet these arise as a consequence of the variation process itself, we speak of a free boundary values variational problem. Such is, for instance, the problem of find
Externí odkaz:
http://arxiv.org/abs/1703.03945