Four-dimensional almost-Einstein manifolds with circulant structures
Abstract
This paper considers a four-dimensional Riemannian manifold with an additional circulant tensor structure Q. We prove that such a manifold is almost-Einstein if the curvature tensor preserves the action of the structure on the last two arguments. Additionally, we examine an associated Riemannian product manifold $(M, g, Q)$ where P=Q2, deriving explicit expressions for the curvature tensor in terms of the metric and the product structure. The sectional and Ricci curvatures of these manifolds are determined using special bases generated by the images of a given vector under the structure Q. Finally, we construct a non-trivial example of a four-dimensional locally product manifold by embedding a four-dimensional hypersurface into a ten-dimensional Euclidean space.
Related
- Weakly Einstein and weakly η-Einstein structures on almost contact metric three-manifolds
- Three-dimensional noncompact trans-Sasakian η-Einstein manifolds
- Smooth Quasi--Einstein Lifts of Locally Embeddable Three-Dimensional CR Manifolds
- Infinitesimmaly homogeneous manifolds with symplectic and almost contact structure groups
- Spectral almost rigidity on Kähler manifolds with positive Ricci lower bound
BibTeX
@misc{dokuzova2026fourdimensional,
title = {{Four-dimensional almost-Einstein manifolds with circulant structures}},
author = {Iva Dokuzova and Georgi Dzhelepov and Dimitar Razpopov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16377},
eprint = {2610.16377},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16377},
}
RIS
TY - UNPB
TI - Four-dimensional almost-Einstein manifolds with circulant structures
AU - Iva Dokuzova
AU - Georgi Dzhelepov
AU - Dimitar Razpopov
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16377
UR - https://arxiv.org/abs/2610.16377
AB - This paper considers a four-dimensional Riemannian manifold with an additional circulant tensor structure Q. We prove that such a manifold is almost-Einstein if the curvature tensor preserves the action of the structure on the last two arguments. Additionally, we examine an associated Riemannian product manifold $(M, g, Q)$ where P=Q^2, deriving explicit expressions for the curvature tensor in terms of the metric and the product structure. The sectional and Ricci curvatures of these manifolds are determined using special bases generated by the images of a given vector under the structure Q. Finally, we construct a non-trivial example of a four-dimensional locally product manifold by embedding a four-dimensional hypersurface into a ten-dimensional Euclidean space.
ER -