Warped product submanifolds of Lorentzian paracosymplectic manifolds
  In this paper we study the warped product submanifolds of a Lorentzian paracosymplectic manifold and obtain some nonexistence results. We show that a warped product semi-invariant submanifold in the form {$M=M_{T}\times_{f}M_{\bot}$} of Lorentzian paracosymplectic manifold such that the characteristic vector field is normal to $M$ is an usual Riemannian product manifold where totally geodesic and totally umbilical submanifolds of warped product are invariant and anti-invariant, respectively. We prove that the distributions involved in the definition of a warped product semi-invariant submanifold are always integrable. A necessary and sufficient condition for a semi-invariant submanifold of a Lorentzian paracosymplectic manifold to be warped product semi-invariant submanifold is obtained. We also investigate the existence and nonexistence of warped product semi-slant and warped product anti-slant submanifolds in a Lorentzian paracosymplectic manifold. 
Selcen Y\"uksel Perkta\c{s}, Erol K{\i}l{\i}\c{c}, Sad{\i}k Kele\c{s}
math.DG