Quasi-Yamabe and Yamabe Solitons on Hypersurfaces of Nearly Kähler Manifolds

Abstract

We establish that if the soliton vector field is the Reeb vector field, then a hypersurface of a nearly Kähler manifold is a quasi-Yamabe soliton if and only if it is a Yamabe soliton. We prove that if a hypersurface of an arbitrary nearly Kähler manifold admits a (quasi)-Yamabe soliton with the Reeb vector field as a soliton vector field, then its scalar curvature is constant and its Reeb flow is isometric, and conversely. Also, such a hypersurface is a Hopf hypersurface. Furthermore, we give a complete classification of such solitons when the ambient manifold is a certain nearly Kähler manifold (six-dimensional unit sphere, product of two three-dimensional unit spheres), a complex space form, and a complex quadric.