Pointwise Bi-Slant Submanifolds in Locally Conformal K\"ahler Manifolds Immersed as Warped Products

Abstract

We study immersions of pointwise bi-slant submanifolds of locally conformal K\"ahler manifolds as warped products. In particular, we establish characterisation theorem for a pointwise bi-slant submanifold of a locally conformal K\"ahler manifold to be immersed as a warped product and show that a necessary condition is that the Lee vector field $B$ is orthogonal to the second factor and the warping function $\lambda$ satisfies $\text{grad}(\ln\lambda)=\frac{1}{2}B^T$, where $B^T$ denotes the tangential part of the Lee vector field. We also extend Chen's inequality for the squared length of the second fundamental form to our case and study the corresponding equality case.