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

Year 2021, Volume: 18 Issue: 2, 72 - 80, 01.11.2021

Ashoke Das Ashis Biswas Bappaditya Debnath

Abstract

The object of the present paper is to study the Riemannian solitons on (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 (LCS)n-manifold admitting (i) R·C = 0, R·K = 0, (ii) E ·C = 0, E ·K = 0, (iii) R·R = 0, R·P = 0, R·E = 0, R·P ∗ = 0, R·M = 0, R ·Wi =0, R ·W∗ i = 0, (iv) E ·R = 0, E ·P = 0, E · E = 0, E ·P ∗ = 0, E ·M = 0, E · Wi = 0 and E · W∗ i = 0.( for all i = 1, 2, ....9). We found that the Riemann soliton on M is shrinking, steady or expanding according to the conditions (i) α 2 − ρ being positive, zero or negative respectively, (ii) [k(n−1) (n − 2) (1+α 2−ρ)−kr−r] being positive, zero or negative respectively and (iv) α 2 − ρ being negative, zero or positive. But for the condition (iii) the Riemann soliton on M is always steady.

Keywords

Reimannian Solution, (LCS)n-manifold, semi-symetric structure

Supporting Institution

NA

Project Number

NA

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