Riemannian semisymmetric almost Kenmotsu manifolds and nullity distributions
Volume 112 / 2014
Annales Polonici Mathematici 112 (2014), 37-46
MSC: Primary 53C15; Secondary 53C25, 53D15.
DOI: 10.4064/ap112-1-3
Abstract
We consider an almost Kenmotsu manifold $M^{2n+1}$ with the characteristic vector field $\xi $ belonging to the $(k,\mu )'$-nullity distribution and $h'\not =0$ 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 $\xi $-Riemannian-semisymmetric. Moreover, if $M^{2n+1}$ is a $\xi $-Riemannian-semisymmetric almost Kenmotsu manifold such that $\xi $ belongs to the $(k,\mu )$-nullity distribution, we prove that $M^{2n+1}$ is of constant sectional curvature $-1$.
