Turkish Journal of Mathematics
DOI
10.3906/mat-1504-73
Abstract
Let $M^{2n+1}$ be an almost co-K\"{a}hler manifold of dimension $>3$ with K\"{a}hlerian leaves. In this paper, we first prove that if $M^{2n+1}$ is locally symmetric, then either it is a co-K\"{a}hler manifold with locally symmetric K\"{a}hlerian leaves, or the Reeb vector field $\xi$ is harmonic and in this case $M^{2n+1}$ is non-co-K\"{a}hler. We also prove that any almost co-K\"{a}hler manifold of dimension $3$ is $\phi$-symmetric if and only if it is locally isometric to either a flat Euclidean space $\mathbb{R}^3$ or a Riemannian product $\mathbb{R}\times N^2(c)$, where $N^2(c)$ denotes a K\"{a}hler surface of constant curvature $c\neq0$.
Keywords
Locally symmetric, $\phi$-symmetric, almost co-K\"{a}hler manifold, K\"{a}hlerian leaves
First Page
740
Last Page
752
Recommended Citation
WANG, YANING
(2016)
"Almost co-K\"{a}hler manifolds satisfying some symmetry conditions,"
Turkish Journal of Mathematics: Vol. 40:
No.
4, Article 3.
https://doi.org/10.3906/mat-1504-73
Available at:
https://journals.tubitak.gov.tr/math/vol40/iss4/3
