zeta-Ricci Soliton on Real Hypersurfaces of Nearly Kaehler 6-Sphere with SSMC

Abstract

The main intention of this paper is to study the real hypersurfaces in nearly Kaehler S6 endowed with a semi-symmetric metric connection. We characterize the real hypersurfaces of the nearly Kaehler S6 admitting semi-symmetric metric connection, and investigate the curvature properties of these submanifolds. Moreover, it is shown that a real hypersurface is congruent to an open segment of a totally-geodesic hypersphere or a tube over an almost complex curve in S6 if such a connected real hypersurface of nearly Kaehler S6 is an zeta -Ricci soliton with the potential vector field xi.