Communications of the
Korean Mathematical Society CKMS

The object of the present paper is to characterize Bach flat $(k,\mu)$-almost co-K\"{a}hler manifolds. It is proved that a Bach flat $(k,\mu)$-almost co-K\"{a}hler manifold is $K$-almost co-K\"{a}hler manifold under certain restriction on $\mu$ and $k$. We also characterize $(k,\mu)$-almost co-K\"{a}hler manifolds with divergence free Cotton tensor.

Keywords: $(k,\mu)$-almost co-K\"{a}hler manifold, Bach tensor, Bach flat tensor, divergence free Cotton tensor

MSC numbers: Primary 53C15, 53C25