Almost Contact B-Metric Structure on 5-Dimensional Nilpotent Lie algebras

Year 2020, Volume: 13 Issue: 2, 87 - 97, 15.10.2020

Şenay Bulut Sevgi Enveş Ermiş

https://doi.org/10.36890/iejg.630746

Abstract

The classification of almost contact $B-$metric manifolds is considered. It is shown that $\mathcal{D}-$homothetic deformation of these manifolds in the class $\mathcal{F}_{i}$ $\left( i=0,1,4,5\right) $ remains in the same the class $\mathcal{F}_{i}$. We study almost contact $B-$metric structure on $5-$dimensional nilpotent Lie algebras. The class of the left invariant almost contact $B-$metric structures on corresponding Lie groups is investigated. Finally, we determine the class of $5-$dimensional nilpotent Lie algebras with almost contact $B-$metric structure.

Keywords

5-dimensional nilpotent lie algebra, almost contact $B-$metric manifold, fundamental tensor

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