Warped product lightlike submanifolds with a slant factor

In the present study, we investigate a new type of warped products on manifolds with indefinite metrics namely, warped product lightlike submanifolds of indefinite Kaehler manifolds with a slant factor.At first, we show that indefinite Kaehler manifolds do not admit any proper warped product semi-slant lightlike submanifolds of the typewhere N T is a holomorphic submanifold, N ⊥ is a totally real submanifold and N θ is a proper slant submanifold.Then, we study warped product semi-slant lightlike submanifolds of the type B × λ N θ , where B = N T × N ⊥ , of an indefinite Kaehler manifold.Following this, we give one non-trivial example for this kind of warped products of indefinite Kaehler manifolds.Then, we establish a geometric estimate for the squared norm of the second fundamental form involving the Hessian of warping function λ for this class of warped products.Finally, we present a sharp geometric inequality for the squared norm of second fundamental form of warped product semi-slant lightlike submanifolds of the type B × λ N θ .