On three dimensional affine Szab\'o manifolds
Differential Geometry
2016-04-21 v1
Abstract
In this paper, we consider the cyclic parallel Ricci tensor condition, which is a necessary condition for an affine manifold to be Szab\'o. We show that, in dimension , there are affine manifolds which satisfy the cyclic parallel Ricci tensor but are not Szab\'o. Conversely, it is known that in dimension , the cyclic parallel Ricci tensor forces the affine manifold to be Szab\'o. Examples of -dimensional affine Szabo manifolds are also given. Finally, we give some properties of Riemannian extensions defined on the cotangent bundle over an affine Szab\'o manifold.
Cite
@article{arxiv.1604.05422,
title = {On three dimensional affine Szab\'o manifolds},
author = {Abdoul Salam Diallo and Silas Longwap and Fortuné Massamba},
journal= {arXiv preprint arXiv:1604.05422},
year = {2016}
}
Comments
14 pages. arXiv admin note: text overlap with arXiv:1604.05420, arXiv:1604.05424