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Affine Szabó connections on smooth manifolds

In this paper, we introduce a new structure, namely, affine Szabó connection. We prove that, on $2$-dimensional affine manifolds, the affine Szabó structure is equivalent to one of the cyclic parallelism of the Ricci tensor. A characterization for locally homogeneous affine Szabó surface is obtained. Examples of two- and three-dimensional affine Szabó manifolds are also given.

preprint2016arXivOpen access
Abdoul Salam DialloFortuné Massamba
math.DG
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Abdoul Salam DialloFortuné Massamba

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