Geodesic
Quaternionic-like structures on a manifold: Note I. 1-integrability and integrability conditions
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 4 (1993) no. 1, pp. 43-52

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

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 integrability conditions are derived. Decompositions of appropriate spaces of curvature tensors are given. In Note II the automorphism groups of these quaternionic-like structures will be considered. 
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     title = {Quaternionic-like structures on a manifold: {Note} {I.} 1-integrability and integrability conditions},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni},
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Alekseevsky, Dmitri V.; Marchiafava, Stefano. Quaternionic-like structures on a manifold: Note I. 1-integrability and integrability conditions. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 4 (1993) no. 1, pp. 43-52. http://geodesic.mathdoc.fr/item/RLIN_1993_9_4_1_a3/