Warped Product Bi-slant Immersions in Kaehler Manifolds

A submanifold M of an almost Hermitian manifold ((widetilde{M},g,J)) is called slant, if for each point (pin M) and (0ne Xin T_p M), the angle between JX and (T_p M) is constant (see Chen in Bull Aust Math Soc 41:135–147, 1990). Later, Carriazo (in: Proceedings of the ICRAMS 2000, Kharagpur, 2000) defined the notion of bi-slant immersions as an extension of slant immersions. In this paper, we study warped product bi-slant submanifolds in Kaehler manifolds and provide some examples of warped product bi-slant submanifolds in some complex Euclidean spaces. Our main theorem states that every warped product bi-slant submanifold in a Kaehler manifold is either a Riemannian product or a warped product hemi-slant submanifold.