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arXiv · 1604.05422

On three dimensional affine Szab\'o manifolds

Abdoul Salam Diallo·Silas Longwap·Fortuné Massamba
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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 $3$, there are affine manifolds which satisfy the cyclic parallel Ricci tensor but are not Szab\'o. Conversely, it is known that in dimension $2$, the cyclic parallel Ricci tensor forces the affine manifold to be Szab\'o. Examples of $3$-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.

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Abdoul Salam Diallo, Silas Longwap, Fortuné Massamba. 2016-04-19. On three dimensional affine Szab\'o manifolds. https://arxiv.org/abs/1604.05422

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