Work

Invariant Monge–Ampère equations on contactified para–Kähler manifolds

Year: 2025

Type: article

Abstract: We develop a method for describing invariant PDEs of Monge–Ampère type in the sense of Lychagin and Morimoto (MAE) on a homogeneous contact manifold N of a semisimple Lie group G , which is the contactification of the homogeneous symplectic manifold $$M = G/H = \textrm{Ad}_G Z \subset \mathfrak {g}$$ M = G / H = Ad G Z ⊂ g , where M is the adjoint orbit of a splittable closed element Z of the Lie algebra $$\mathfrak {g}= {{\,\textrm{Lie}\,}}(G)$$ g = Lie ( G ) . The method is then applied to a ten-dimensional semisimple orbit M of the exceptional Lie group $$\textsf{G}_2$$ G 2 and a complete list of mutually non-equivalent MAEs on N is obtained.

Source: Annals of Global Analysis and Geometry

DOI: 10.1007/s10455-025-09999-8

Authors: Dmitri Alekseevsky, Gianni Manno, Giovanni Moreno

Institutions: Moscow Institute of Physics and Technology, Politecnico di Torino, University of Warsaw

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Politecnico di Torino, Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni