Riemannian semisymmetric almost Kenmotsu manifolds and nullity distributions
Tom 112 / 2014
Annales Polonici Mathematici 112 (2014), 37-46
MSC: Primary 53C15; Secondary 53C25, 53D15.
DOI: 10.4064/ap112-1-3
Streszczenie
We consider an almost Kenmotsu manifold 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.