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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.

##### MSC:
 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