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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...

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