Preprint Article Version 1 This version is not peer-reviewed

Four-Dimensional Almost Einstein Manifolds with Skew-Circulant Structres

Version 1 : Received: 10 June 2019 / Approved: 13 June 2019 / Online: 13 June 2019 (05:36:28 CEST)

How to cite: Dokuzova, I.; Razpopov, D. Four-Dimensional Almost Einstein Manifolds with Skew-Circulant Structres. Preprints 2019, 2019060109 (doi: 10.20944/preprints201906.0109.v1). Dokuzova, I.; Razpopov, D. Four-Dimensional Almost Einstein Manifolds with Skew-Circulant Structres. Preprints 2019, 2019060109 (doi: 10.20944/preprints201906.0109.v1).

Abstract

We consider a four-dimensional Riemannian manifold M equipped with an additional tensor structure S, whose fourth power is minus identity and the second power is an almost complex structure. In a local coordinate system the components of the metric g and the structure S form skew-circulant matrices. Both structures S and g are compatible, such that an isometry is induced in every tangent space of M. By a special identity for the curvature tensor, generated by the Riemannian connection of g, we determine classes of an Einstein manifolds and an almost Einstein manifolds. For such manifolds we obtain propositions for the sectional curvatures of some special 2-planes in a tangent space of M. We consider an almost Hermitian manifold associated with the studied manifold and find conditions for g, under which it is a Kähler manifold. We construct some examples of the considered manifolds on Lie groups.

Subject Areas

Riemannian manifold; Einstein manifold; sectional curvatures; Ricci curvature; Lie group

Comments (0)

We encourage comments and feedback from a broad range of readers. See criteria for comments and our diversity statement.

Leave a public comment
Send a private comment to the author(s)
Views 0
Downloads 0
Comments 0
Metrics 0


×
Alerts
Notify me about updates to this article or when a peer-reviewed version is published.