Some solitons on anti-invariant submanifold of LP-Kenmotsu manifold admitting Zamkovoy connection

Abstract

In this paper we prove some curvature properties of anti-invariant submanifold of Lorentzian para-Kenmotsu manifold (briefly, LP-Kenmotsu manifolds) with respect to Zamkovoy connection (∇∗). Next, we study Einstein soliton on anti-invariant submanifold of LP-Kenmotsu manifold with respect to Zamkovoy connection. Further, we study η-Einstein soliton on this submanifold with respect to Zamkovoy connection under different curvature conditions. Finally, we give an example of anti-invariant submanifold of 5-dimensional LP-Kenmotsu manifold admitting η-Einstein soliton with respect to ∇∗ and verify a relation on it.

Keywords

• lorentzian para-kenmotsu manifold
• anti-invariant submanifold
• zamkovoy connection
• η-einstien soliton
• concircular curvature tensor