On Submanifolds of $N(k)$-Quasi Einstein Manifolds with a Type of Semi-Symmetric Metric Connection

Abstract

In this study, we consider the $ N(k)- $quasi Einstein manifolds with respect to a type of semi-symmetric metric connection. We suppose that the generator of $ N(k)- $quasi-Einstein manifolds is parallel with respect to semi-symmetric metric connection and we classify such manifolds. In addition, we consider the submanifolds of a $ N(k)- $quasi Einstein manifold and we obtain some conditions on the totally geodesic and the totally umbilic submanifolds. Finally, we consider a para-Kenmotsu space form as an example of $ N(k)- $quasi-Einstein manifolds.

Keywords

• n(k)-quasi einstein manifolds
• totally geodesic
• totally umbilical
• para-kenmotsu