Archivio Istituzionale della RicercaWe 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=AdGZ, where M is the adjoint orbit of a splittable closed element Z of the Lie algebra g=Lie(G). The method is then applied to a ten-dimensional semisimple orbit M of the exceptional Lie group G2 and a complete list of mutually non-equivalent MAEs on N is obtained.
Invariant Monge-Ampère equations on contactified para-Kähler manifolds / Alekseevsky, D.; Manno, G.; Moreno, G.. - In: ANNALS OF GLOBAL ANALYSIS AND GEOMETRY. - ISSN 1572-9060. - 67:4(2025). [10.1007/s10455-025-09999-8]
Invariant Monge-Ampère equations on contactified para-Kähler manifolds
Manno G.;
2025
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=AdGZ, where M is the adjoint orbit of a splittable closed element Z of the Lie algebra g=Lie(G). The method is then applied to a ten-dimensional semisimple orbit M of the exceptional Lie group G2 and a complete list of mutually non-equivalent MAEs on N is obtained.
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https://hdl.handle.net/11583/3003787
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