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

Authors : Şenay Bulut, Vildan Korucu Akan

Pages : 206-217

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Publication Date : 2023-10-31

Article Type : Research Paper

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