Geodesic
Affine Connections whose Ricci Tensors are Cyclic Parallels
Journal for geometry and graphics, Tome 28 (2024) no. 2, pp. 169-179
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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.
Classification : 53A15, 53B05, 53C05
Mots-clés : Affine connections, cyclic parallel Ricci tensor, Einstein like manifolds 
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     author = {M. M. A. Abdou and M. E. B. Mame and A. S. Diallo and L. A. Sid'Ahmed},
     title = {Affine {Connections} whose {Ricci} {Tensors} are {Cyclic} {Parallels}},
     journal = {Journal for geometry and graphics},
     pages = {169--179},
     year = {2024},
     volume = {28},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JGG_2024_28_2_JGG_2024_28_2_a2/}
}
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M. M. A. Abdou; M. E. B. Mame; A. S. Diallo; L. A. Sid'Ahmed. Affine Connections whose Ricci Tensors are Cyclic Parallels. Journal for geometry and graphics, Tome 28 (2024) no. 2, pp. 169-179. http://geodesic.mathdoc.fr/item/JGG_2024_28_2_JGG_2024_28_2_a2/