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)
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
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
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.
Keywords
Riemannian manifold; Einstein manifold; sectional curvatures; Ricci curvature; Lie group
Subject
Computer Science and Mathematics, Geometry and Topology
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
