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## 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 $M^{2n+1}$ 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 $-1$.

#### Autorzy

• Yaning WangCollege of Mathematics and Information Science
Henan Normal University
Xinxiang 453007, Henan, P.R. China
e-mail
• Ximin LiuSchool of Mathematical Sciences
Dalian University of Technology
Dalian 116024, Liaoning, P.R. China
e-mail

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