Geodesic
On Weakly $W_3$-Symmetric Manifolds
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 50 (2011) no. 1, pp. 53-71.

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The object of the present paper is to study weakly $W_3$-symmetric manifolds and its decomposability with the existence of such notions. Among others it is shown that in a decomposable weakly $W_3$-symmetric manifold both the decompositions are weakly Ricci symmetric.
Classification : 53B05, 53B35, 53C15, 53C25
Keywords: weakly $W_3$-symmetric manifold; $W_3$-curvature tensor; decomposable manifold; scalar curvature; totally umbilical hypersurfaces; totally geodesic; mean curvature 
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Hui, Shyamal Kumar. On Weakly $W_3$-Symmetric Manifolds. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 50 (2011) no. 1, pp. 53-71. http://geodesic.mathdoc.fr/item/AUPO_2011__50_1_a5/