B.-Y. Chen's inequality for $CR$-warped products in a locally conformal   Kaehler space form
  n this paper, we obtain a geometric inequality between the length of the second fundamental form and the length of Lee form in terms of the warping function for a CR-warped product submanifold in a locally conformal Kaehler space form. The equality case is also investigated. Furthermore, the inequality is discussed for the important subclass of locally conformal Kaehler manifolds i.e., Vaisman manifold. 
Siraj Uddin, Khushwant Singh, Fatimah Alghamdi, Cengizhan Murathan
math.DG