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

Bělohlávková, Jana; Mikeš, Josef; Pokorná, Olga

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].

Reviewer: A.Ferrandez (Espinardo)

MSC:

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

Keywords:

4-planar mappings; almost quaternionic spaces; Hermitian spaces