Bulletin of the
Korean Mathematical Society BKMS

Many differential geometric properties of a submanifold of a Kaehler manifold are conceived via canonical structure tensors $T$ and $F$ on the submanifold. For instance, a $CR$-submanifold of a Kaehler manifold is a $CR$-product if and only if $T$ is parallel on the submanifold (c.f. \cite{ch1}). Warped product submanifolds are generalized version of $CR$-product submanifolds. Therefore, it is natural to see how the non-triviality of the covariant derivatives of $T$ and $F$ gives rise to warped product submanifolds. In the present article, we have worked out characterizations in terms of $T$ and $F$ under which a contact $CR$- submanifold of a Kenmotsu manifold reduces to a warped product submanifold.

Keywords: $CR$-submanifold, warped product, Kenmotsu manifold

MSC numbers: 53C25, 53D15