Fueter and hypercomplex structures on smooth manifolds (Q1318907)

The author compares Fueter structures on manifolds with other types of structures, so \(f\)-structures defined by \textit{K. Yano} [Tensor, New Ser., 14, 99-109 (1963; Zbl 0122.407)] as well as quaternionic and other hypercomplex structures. Here a Fueter structure is defined by Fueter mappings \(F\); these are generated by holomorphic mappings \(\varphi\) of the upper half plane; the variable \(x = (x_ 0, \dots, x_{n-1})\in \mathbb{R}^ n\) is first reduced to \((x_ 0, y)\) by \(y = | (x_ 1, \dots, x_{n - 1}) |\) and then blown up by \[ f \bigl( \varphi (x) \bigr) = \text{Re} \varphi (x_ 0, y) + \sum e_ j x_ j \bigl( \text{Im} \varphi (x_ 0, y) \bigr)/y. \] [For further notations and definitions see the paper itself.].