On Quasi-para-Sasakian Structures on 5-dimensions

Abstract

In this study, we investigate the existence of quasi-para-Sasakian structures on five dimensional nilpotent Lie algebras. There are six non-abelian nilpotent Lie algebras. We show that quasi-para-Sasakian structures exist only on one of these algebras. Quasi-para-Sasakian structures correspond to the class G_5+G_8 in the classification of almost paracontact metric structures. We show that a quasi-para-Sasakian structure on a five dimensional nilpotent Lie algebra is either in G_5 or G_8.