On pseudosymmetric manifolds

By Absos Ali Shaikh, R. Deszcz, Marin Hotlos, Jan Jelwicki, H. Kundu. 2014

69 citations recorded by the source corpus.

In the literature, there are two different notions of pseudosymmetric manifolds, one by Chaki [7] and other by Deszcz [16], and there are many papers related to these notions. The object of the present paper is to deduce necessary and sufficient conditions for a Chaki pseudosymmetric [7] (resp. pseudo Ricci symmetric [8]) manifold to be Deszcz pseudosymmetric (resp. Ricci pseudosymmetric). We also study the necessary and sufficient conditions for a weakly symmetric [58] (resp. weakly Ricci symmetric [59]) manifold by Tam\'assy and Binh to be Deszcz pseudosymmetric (resp. Ricci pseudosymmetric). We also obtain the reduced form of the defining condition of weakly Ricci symmetric manifolds by Tam\'assy and Binh [59]. Finally we give some examples to show the independent existence of such types of pseudosymmetry which also ensure the existence of Roter type and generalized Roter type manifolds and the manifolds with recurrent curvature 2-form ([2], [29]) associated to various curvature tensors.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/de64699ad594379c2c535e448254e1c453c30bad

Citations in the corpus

• On equivalency of various geometric structures (2013, unknown): “generalized T-recurrent if Sκ(X,Π,Φ,Ψ,Θ)T = 0 for all X ∈ χ(M) and some 1-forms Π, Φ, Ψ and Θ, called the associated 1-forms. Obviously this operator is of 1st type and non-extendible. Definition 4.8. [5] Consider the operator CP(X,Π) : T 0 k → T 0 k+1 defined by CP(X,Π)T = ∇XT −2Π(X)⊗ T − Π X ·T, Π i”