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A report on quaternionic-like structures on a manifold. (English) Zbl 0855.53018
Summary: This is a report on some recent results concerning six quaternionic-like structures that are defined on a manifold \(M\) (almost quaternionic, hypercomplex, unimodular quaternionic, unimodular hypercomplex, Hermitian quaternionic, Hermitian hypercomplex). The interrelations between them and their automorphism groups are considered in the framework of the general theory of \(G\)-structures. Some applications of the general results to other classical structures and some open problems are indicated.

53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C55 Global differential geometry of Hermitian and Kählerian manifolds
53C10 \(G\)-structures
53C05 Connections (general theory)
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
57R20 Characteristic classes and numbers in differential topology