Journal for Geometry and Graphics 28 (2024), No. 2, 169--179
Copyright by the authors licensed under CC BY SA 4.0
Affine Connections whose Ricci Tensors are Cyclic Parallels
Moulaye M. A. Abdou
Université de Nouakchott, Nouakchott, Mauretania
moulo026@gmail.com
Mohamed El Boukhary Mame
Université de Nouakchott, Nouakchott, Mauretania
ouldemame@gmail.com
Abdoul Salam Diallo
Université Alioune Diop, Bambey, Sénégal
abdoulsalam.diallo@uadb.edu.sn
Lessiad Ahmed Sid'Ahmed
Université de Nouakchott, Nouakchott, Mauretania
lessiadahmed@gmail.com
This paper focuses on the situation where ∇ is an affine connection on a smooth manifold M. We give necessary and sufficient conditions on the coefficients of the affine connection ∇ on an 3-dimensional affine manifold such that the Ricci tensor of ∇ is cyclic parallel. Examples of three families affine connections which have cyclic parallel Ricci tensors are given on an 3-dimensional affine manifold.
Keywords: Affine connections, cyclic parallel Ricci tensor, Einstein like manifolds.
MSC: 53A15; 53B05, 53C05.
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