Riemannian semisymmetric almost Kenmotsu manifolds and nullity distributions

Yaning Wang¹ ; Ximin Liu²

¹ College of Mathematics and Information Science Henan Normal University Xinxiang 453007, Henan, P.R. China
² School of Mathematical Sciences Dalian University of Technology Dalian 116024, Liaoning, P.R. China

Annales Polonici Mathematici, Tome 112 (2014) no. 1, pp. 37-46

Résumé

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 $-1$.

Détail

DOI : 10.4064/ap112-1-3

Keywords: consider almost kenmotsu manifold characteristic vector field belonging nullity distribution prove locally isometric riemannian product dimensional manifold constant sectional curvature flat n dimensional manifold provided riemannian semisymmetric moreover riemannian semisymmetric almost kenmotsu manifold belongs nullity distribution prove constant sectional curvature