The object of the present paper is to study anti-invariant submanifolds of Lorentzian para-Kenmotsu manifold (briefly, LP-Kenmotsu manifold) with respect to the Zamkovoy connection. We prove that if an anti-invariant submanifold M of LP-Kenmotsu manifold contains a conformal Ricci soliton with collinear Reeb vector field, then M is η-Einstein. We also study conformal η-Ricci soliton on this submanifold with the Zamkovoy connection satisfying the curvature conditions: (ξ.)R∗ .S∗ = 0, (ξ.)S∗ .R∗ and (ξ.)S∗ .P∗ = 0. To validate some of our results, we construct a non-trivial example of anti-invariant submanifold of 5-dimensional LP-Kenmotsu manifolds admitting conformal η-Ricci soliton with respect to the Zamkovoy connection.
Mandal et al. (Wed,) studied this question.