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Differential geometry of quaternionic manifolds. (English) Zbl 0616.53023

Let \(H\) be the usual quaternion algebra, and \(G\) the maximal subgroup \(\text{GL}(n,H)\cdot \text{GL}(1,H)\) of \(\text{GL}(4n, \mathbb R)\). A quaternionic manifold is, by definition, a pair of a \(4n\)-dimensional \(C^{\infty}\)-manifold \(M\) and a \(G\)-structure over \(M\) admitting a torsionfree connection.
This paper consists of an exposition of a theory of quaternionic manifolds which has been announced by the author in Symp. Math. 26, 139–151 (1982; Zbl 0534.53030) and in Global Riemannian geometry, Proc. Symp., Durham/Engl. 1982, 65–74 (1984; Zbl 0516.53022).
Reviewer: T.Ochiai

MSC:

53C10 \(G\)-structures
53C05 Connections (general theory)
53B35 Local differential geometry of Hermitian and Kählerian structures
53C26 Hyper-Kähler and quaternionic Kähler geometry, “special” geometry
53C28 Twistor methods in differential geometry
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References:

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