CONFORMAL η−RICCI SOLİTONS ON ANTI-INVARIANT SUBMANIFOLD OF LP-KENMOTSU MANIFOLD ENDOWED WITH THE ZAMKOVOY CONNECTION

Abstract

The object of the present paper is to study anti-invariant submanifolds of LP-Kenmotsu manifold with respect to the Zamkovoy connection. We prove that if an anti-invariant submanifoldMof LP-Kenmotsu manifold contains a conformal Ricci soliton with collinear Reeb vector field then the manifold is η-Einstein. We also study conformal η-Ricci soliton on this manifold 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-ivariant submanifold of 5-dimensional LP-Kenmotsu manifolds admitting conformal η-Ricci soliton with respect to the Zamkovoy connection.