On 3-dimensional almost Einstein manifolds with circulant structures

DOI10.3906/MAT-1904-97zbMATH Open1451.53040arXiv2005.13476OpenAlexW3029594134MaRDI QIDQ4971507

Iva Dokuzova

Publication date: 12 October 2020

Published in: Turkish Journal of Mathematics (Search for Journal in Brave)

Abstract: A 3-dimensional Riemannian manifold equipped with a tensor structure of type $(1,1)$, whose third power is the identity, is considered. This structure and the metric have circulant matrices with respect to some basis, i.e., these structures are circulant. An associated manifold, whose metric is expressed by both structures, is studied. Three classes of such manifolds are considered. Two of them are determined by special properties of the curvature tensor of the manifold. The third class is composed by manifolds whose structure is parallel with respect to the Levi-Civita connection of the metric. Some geometric characteristics of these manifolds are obtained. Examples of such manifolds are given.

Full work available at URL: https://arxiv.org/abs/2005.13476

zbMATH Keywords

Riemannian manifoldLie groupRicci curvatureEinstein manifoldindefinite metric

Mathematics Subject Classification ID

Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Lie algebras of Lie groups (22E60) General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15) Local Riemannian geometry (53B20) Local differential geometry of Lorentz metrics, indefinite metrics (53B30)

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