Critical point equation on N(k)-contact manifolds

The object of the present paper is to characterize N(k)-contact metric manifolds satisfying the *-critical point equation. It is proved that, if (g, λ) is a non-constant solution of the *-critical point equation of a non-compact N(k)-contact metric manifold, then (1) the manifold M is locally isometric to the Riemannian product of a at (n + 1)-dimensional manifold and an n-dimensional manifold of positive curvature 4 for n > 1 and at for n = 1, (2) the manifold is *-Ricci at and (3) the function λ is harmonic. The result is also verified by an example.