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

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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 
@article{KJM_2019_43_3_a10,
     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/}
}
TY  - JOUR
AU  - Absos Ali Shaikh
AU  - Haradhan Kundu
TI  - On Generalized Roter Type Manifolds
JO  - Kragujevac Journal of Mathematics
PY  - 2019
SP  - 471 
VL  - 43
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/KJM_2019_43_3_a10/
LA  - en
ID  - KJM_2019_43_3_a10
ER  - 
%0 Journal Article
%A Absos Ali Shaikh
%A Haradhan Kundu
%T On Generalized Roter Type Manifolds
%J Kragujevac Journal of Mathematics
%D 2019
%P 471 
%V 43
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/KJM_2019_43_3_a10/
%G en
%F KJM_2019_43_3_a10
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/