Some warped product submanifolds of a Kenmotsu manifold
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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 mani- fold is a CR-product if and only if T is parallel on the submanifold (c.f. [2]). 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 subman- ifolds. 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.
Abstract
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 mani- fold is a CR-product if and only if T is parallel on the submanifold (c.f. [2]). 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 subman- ifolds. 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.
참고문헌 (15)
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