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Why do quaternionic spaces lack complex structures? (English) Zbl 0858.57031

The author reviews the notion of special structures on manifolds with emphasis on almost complex structures. He proves that quaternionic spaces do not have an invariant almost complex structure and he discusses why. Many examples are given.
Reviewer: F.Gomez (Malaga)

MSC:

57R15 Specialized structures on manifolds (spin manifolds, framed manifolds, etc.)
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
57-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to manifolds and cell complexes
53-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to differential geometry
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