Generic Warped Product Submanifolds in Nearly Kaehler Manifolds

Warped product manifolds provide excellent setting to model space-time near black holes or bodies with large gravitational force (cf. [1], [2], [14]). Recently, results are published exploring the existence (or non-existence) of warped product submanifolds in Kaehlerian and contact settings (cf. [6], [17], [20]). To continue the sequel, we have considered warped product submanifolds of nearly Kaehler manifolds with one of the factors a holomorphic submanifold. Such submanifolds are generic submanifolds in the sense of B. Y. Chen [5] and provide a generalization of CR and semi-slant submanifolds. It is shown that nearly Kaehler manifolds do not admit non-trivial warped product generic submanifolds, thereby generalizing the results of Chen [6] and Sahin [20]. However, non-trivial generic warped products (obtained by reversing the two factors of warped product generic submanifolds) exist in nearly Kaehler manifolds (cf. [21]). Some interesting results on the geometry of these submanifolds are obtained in the paper. MSC 2000: 53C40, 53C42, 53C15