Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed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)
Version 2 : Received: 27 May 2020 / Approved: 28 May 2020 / Online: 28 May 2020 (02:58:44 CEST)

A peer-reviewed article of this Preprint also exists.

Dokuzova, I., Razpopov, D. Four-dimensional almost Einstein manifolds with skew-circulant stuctures. J. Geom. 111, 9 (2020). https://doi.org/10.1007/s00022-020-0521-z Dokuzova, I., Razpopov, D. Four-dimensional almost Einstein manifolds with skew-circulant stuctures. J. Geom. 111, 9 (2020). https://doi.org/10.1007/s00022-020-0521-z

Journal reference: Journal of Geometry 2020, 111
DOI: 10.1007/s00022-020-0521-z

Abstract

We consider a four-dimensional Riemannian manifold M with an additional structure S, whose fourth power is minus identity. 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 Einstein and almost Einstein manifolds. For such manifolds we obtain propositions for the sectional curvatures of some characteristic 2-planes in a tangent space of M. We consider a Hermitian manifold associated with the studied manifold and find conditions for g, under which it is a K\"{a}hler 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 (1)

Comment 1
Received: 28 May 2020
Commenter: Iva Dokuzova
Commenter's Conflict of Interests: Author
Comment: Theorem 8. was corrected. There was a technical errors. The proof of the Proposition 1 was corrected in order to be shorter. Corollary 1 was corrected.
+ Respond to this comment

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 1
Metrics 0


×
Alerts
Notify me about updates to this article or when a peer-reviewed version is published.
We use cookies on our website to ensure you get the best experience.
Read more about our cookies here.