4 papers · 1 filter
Conformally homogeneous Lorentzian spaces
Dmitri V. Alekseevsky, Anton S. Galaev
We prove that if a 1-connected non-conformally flat conformal Lorentzian manifold admits a connected essential transitive group of conformal transformations, then there exi…
Third-order affine-invariant (systems of) PDEs in two independent variables as vanishing of the Fubini-Pick invariant
Dmitri Alekseevsky, Gianni Manno, Giovanni Moreno
In this paper we study order (system of) PDEs in two independent variables and one unknown function that are invariant with respect to the group of affi…
Projectively and affinely invariant PDEs on hypersurfaces
Dmitri V. Alekseevsky, Gianni Manno, Giovanni Moreno
In [Alekseevsky, Gutt, Manno, Moreno: "A general method to construct invariant PDEs on homogeneous manifolds", Communications in Contemporary Mathematics (2021)] the authors have d…
Invariant Monge-Ampère equations on contactified para-Kähler manifolds
Dmitri Alekseevsky, Gianni Manno, Giovanni Moreno
We develop a method for describing invariant Monge-Ampère equations in the sense of V. Lychagin and T. Morimoto (MAE) on a homogeneous contact manifold of a semisimple Lie gro…