Some affine properties of the \(k\)-symplectic manifolds (Q1380832)

The notion of \(k\)-symplectic manifold was introduced by the author in his Ph. D. Thesis. Its geometry was developed in the author's papers [\textit{A. Awane}, J. Math. Phys. 33, 4046-4052 (1992; Zbl 0781.53024); J. Geom. Phys 13, 139-157 (1994; Zbl 0795.58015)] and in the reviewer's paper [\textit{M. Puta}, Tensor, New Ser. 47, 109-115 (1988; Zbl 0677.53042)]. In the note under review, some locally affine properties of \(k\)-symplectic manifolds are introduced and some of their geometrical and topological implications are nicely pointed out.