Geodesic
On Generalized Roter Type Manifolds
Kragujevac Journal of Mathematics, Tome 43 (2019) no. 3, p. 471 .

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In the literature of Riemannian geometry there are many conditions for the equivalency of semisymmetric (resp., pseudosymmetric) and Ricci-semisymmetric (resp., Ricci-pseudosymmetric) manifolds. The object of the present paper is to investigate a sufficient condition for the equivalency of semisymmetric (resp., pseudosymmetric) and Ricci-semisymmetric (resp., Ricci-pseudosymmetric) manifolds. It is shown that generalized Roter type condition is a sufficient condition for the equivalency of such structures. Also we obtain alternative proofs of the theorems as given by Deszcz and his coauthors (\cite{ACDE98} and \cite{DHS99}) for the equivalency of such structures. Finally the existence of manifolds satisfying generalized Roter type condition is ensured by some non-trivial examples.
Classification : 53B20, 53B30 53C25, 53C50
Keywords: Conformally flat manifold, Einstein manifold, generalized Einstein manifold, Roter type condition, generalized Roter type condition, curvature restricted geometric structures, semisymmetric manifold, pseudosymmetric manifold 
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     author = {Absos Ali Shaikh and Haradhan Kundu},
     title = {On {Generalized} {Roter} {Type} {Manifolds}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {471 },
     publisher = {mathdoc},
     volume = {43},
     number = {3},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2019_43_3_a10/}
}
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Absos Ali Shaikh; Haradhan Kundu. On Generalized Roter Type Manifolds. Kragujevac Journal of Mathematics, Tome 43 (2019) no. 3, p. 471 . http://geodesic.mathdoc.fr/item/KJM_2019_43_3_a10/