Riemann Solutions (LCS)n-Manifolds Admitting Different Semi-Symmetric Structures

Authors : Ashoke DAS, Ashis BİSWAS, Bappaditya DEBNATH

Pages : 72-80

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Publication Date : 2021-11-01

Article Type : Research Paper

Abstract :The object of the present paper is to study the Riemannian solitons on insert ignore into journalissuearticles values(LCS);nmanifolds and we observed in this case the Riemann soliton on M is shrinking, steady or expanding according to α 2−ρ being positive, zero or negative respectively. Here also we discussed the Riemann solitons in insert ignore into journalissuearticles values(LCS);n-manifold admitting insert ignore into journalissuearticles values(i); R·C = 0, R·K = 0, insert ignore into journalissuearticles values(ii); E ·C = 0, E ·K = 0, insert ignore into journalissuearticles values(iii); R·R = 0, R·P = 0, R·E = 0, R·P ∗ = 0, R·M = 0, R ·Wi =0, R ·W∗ i = 0, insert ignore into journalissuearticles values(iv); E ·R = 0, E ·P = 0, E · E = 0, E ·P ∗ = 0, E ·M = 0, E · Wi = 0 and E · W∗ i = 0.insert ignore into journalissuearticles values( for all i = 1, 2, ....9);. We found that the Riemann soliton on M is shrinking, steady or expanding according to the conditions insert ignore into journalissuearticles values(i); α 2 − ρ being positive, zero or negative respectively, insert ignore into journalissuearticles values(ii); [kinsert ignore into journalissuearticles values(n−1); insert ignore into journalissuearticles values(n − 2); insert ignore into journalissuearticles values(1+α 2−ρ);−kr−r] being positive, zero or negative respectively and insert ignore into journalissuearticles values(iv); α 2 − ρ being negative, zero or positive. But for the condition insert ignore into journalissuearticles values(iii); the Riemann soliton on M is always steady.
Keywords : Reimannian Solution LCS, n manifold, semi symetric structure