Riemannian semisymmetric almost Kenmotsu manifolds and nullity distributions

Yaning Wang ; Ximin Liu

Annales Polonici Mathematici, Tome 111 (2014), p. 37-46 / Harvested from The Polish Digital Mathematics Library

Résumé

We consider an almost Kenmotsu manifold $M^{2n+1}$ with the characteristic vector field ξ belonging to the (k,μ)’-nullity distribution and h’ ≠ 0 and we prove that $M^{2n+1}$ is locally isometric to the Riemannian product of an (n+1)-dimensional manifold of constant sectional curvature -4 and a flat n-dimensional manifold, provided that $M^{2n+1}$ is ξ-Riemannian-semisymmetric. Moreover, if $M^{2n+1}$ is a ξ-Riemannian-semisymmetric almost Kenmotsu manifold such that ξ belongs to the (k,μ)-nullity distribution, we prove that $M^{2n+1}$ is of constant sectional curvature -1.

Détail

Publié le : 2014-01-01

Zbl 1310.53026

EUDML-ID : urn:eudml:doc:281045