On 4-planar mappings of special almost antiquaternionic spaces.(English)Zbl 1013.53022

Slovák, Jan (ed.) et al., The proceedings of the 20th winter school “Geometry and physics”, Srní, Czech Republic, January 15-22, 2000. Palermo: Circolo Matematico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 66, 97-103 (2001).
In this paper it is shown that, under a local condition, an equiaffine space $$A_n$$ admits a 4-planar mapping on: (i) an antiquaternionic Hermitian space $$V_n$$ if and only if there exists a regular tensor $$a^{ij}$$ on $$A_n$$ satisfying three suitable conditions; (ii) a Hermitian almost quaternionic space $$V_n$$ if and only if a certain system of ordinary differential equations of Cauchy type is solvable with respect to the unknown functions $$a^{ij}$$.
For the entire collection see [Zbl 0961.00020].

MSC:

 53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.) 53A15 Affine differential geometry