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
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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 (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...