Riemannian $\Pi-$Structure on $5-$Dimensional Nilpotent Lie Algebras

Abstract

The object of our investigations is to classify 5-dimensional nilpotent Lie algebras with two different Riemannian $\Pi-$structures. It is shown that the Lie groups corresponding to the Lie algebras $\mathfrak{g} _{i}$ equipped with two different Riemannian $\Pi-$structures is not para-Sasaki-like. Moreover, we investigate whether the considered manifolds admit Ricci-like solitons and whether they are $\eta-$Einstein manifolds.

Keywords

• Para-Sasaki-like manifold
• Ricci-like soliton
• Riemannian $\Pi-$manifold
• Five dimensional nilpotent Lie algebras

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