*- Critical point equation on N(k)-contact manifolds

Abstract

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 flat (n + 1)-dimensional manifold and an n-dimensional manifold of positive curvature 4 for n > 1 and flat for n = 1, (2) the manifold is * -Ricci flat and (3) the function λ is harmonic. The result is also verified by an example.2000 Mathematics Subject Classification: 53C25, 53C15.

$N(k)$-contact metric as $\ast$-conformal Ricci soliton

“…In 2014, the notion of * -Ricci soliton [12] was introduced and further widely studied by several authors. In 2019, the notion of * -critical point equation [8] was introduced and further studied by the authors in [9]. In this paper, we study the notion of * -conformal Ricci soliton defined as Definition 1.1.…”