Resumen de Warped product lightlike submanifolds with a slant factor
Megha Pruthi, Sangeet Kumar
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. First, we show that indefinite Kaehler manifolds do not admit any proper warped product semi-slant lightlike submanifolds of the type NT ×λ Nθ, Nθ ×λ NT , N⊥ ×λ Nθ and Nθ ×λ N⊥, where NT is a holomorphic submanifold, N⊥ is a totally real submanifold and Nθ is a proper slant submanifold. Then, we study warped product semi-slant lightlike submanifolds of the type B ×λ Nθ, where B = NT × 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 Nθ.
