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Quaternionic-like structures on a manifold: Note I. 1-integrability and integrability conditions

Dmitri V. Alekseevsky; Stefano Marchiafava — 1993

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

This Note will be followed by a Note II in these Rendiconti and successively by a wider and more detailed memoir to appear next. Here six quaternionic-like structures on a manifold $M$ (almost quaternionic, hypercomplex, unimodular quaternionic, unimodular hypercomplex, Hermitian quaternionic, Hermitian hypercomplex) are defined and interrelations between them are studied in the framework of general theory of G-structures. Special connections are associated to these structures. 1-integrability and...

Quaternionic-like structures on a manifold: Note II. Automorphism groups and their interrelations

Dmitri V. Alekseevsky; Stefano Marchiafava — 1993

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We consider different types of quaternionic-like structures. The interrelations between automorphism groups of the subordinated structures and of some admissible connections are studied. A characterization of automorphisms of a quaternionic structure as some kind of projective transformations is given. General results on harmonicity of an automorphism of some $G$ -structure are obtained and applied to the case of an almost Hermitian quaternionic structure. Different noteworthy transformations groups...

Contact geometry of multidimensional Monge-Ampère equations: characteristics, intermediate integrals and solutions

Dmitri V. Alekseevsky; Ricardo Alonso-Blanco; Gianni Manno; Fabrizio Pugliese — 2012

Annales de l’institut Fourier

We study the geometry of multidimensional scalar $2^{n d}$ order PDEs (i.e. PDEs with $n$ independent variables), viewed as hypersurfaces $ℰ$ in the Lagrangian Grassmann bundle $M^{(1)}$ over a $(2 n + 1)$ -dimensional contact manifold $(M, 𝒞)$ . We develop the theory of characteristics of $ℰ$ in terms of contact geometry and of the geometry of Lagrangian Grassmannian and study their relationship with intermediate integrals of $ℰ$ . After specializing such results to general Monge-Ampère...

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Currently displaying 1 – 3 of 3

Quaternionic-like structures on a manifold: Note I. 1-integrability and integrability conditions

Quaternionic-like structures on a manifold: Note II. Automorphism groups and their interrelations

Contact geometry of multidimensional Monge-Ampère equations: characteristics, intermediate integrals and solutions