Einstein-Type Metrics on Almost Kenmotsu Manifolds.

This article aims to classify the Einstein-type metrics on Kenmotsu and almost Kenmotsu manifolds. In Kenmotsu case, we find that it is T-Einstein. Also, if the manifold is complete and the scalar curvature remains invariant along the Reeb vector field, then either, it is isometric to the hyperbolic space H 2 n + 1 (1) or, the warped product M ~ × γ R , provided ζ ψ ≠ ψ . Next, we investigate non-Kenmotsu (κ , μ) ′ -almost Kenmotsu manifolds obeying the Einstein-type metrics and give some classification. Finally, we establish that if (ψ , g) is a non-trivial solution of Einstein-type metrics with smooth function ψ which is constant along the Reeb vector field on almost Kenmotsu 3-H-manifold, then either, it is locally isometric to the hyperbolic space H 3 (1) or, the Riemannian product H 2 (4) × R . Finally, we construct several non-trivial examples to verify our main results. [ABSTRACT FROM AUTHOR]