η-Ricci solitons on Lorentzian para-Sasakian manifolds | Zendy

Adara M. Blaga | Zendy

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η-Ricci solitons on Lorentzian para-Sasakian manifolds

Author(s) -

Adara M. Blaga

Publication year - 2016

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil1602489b

Subject(s) - mathematics , ricci curvature , manifold (fluid mechanics) , vector field , riemann curvature tensor , ricci decomposition , pure mathematics , curvature of riemannian manifolds , ricci flat manifold , curvature , mathematical analysis , mathematical physics , einstein manifold , einstein , soliton , scalar curvature , sectional curvature , physics , geometry , nonlinear system , quantum mechanics , mechanical engineering , engineering

We consider η-Ricci solitons on Lorentzian para-Sasakian manifolds satisfying certain curvature conditions: R(ξ,X) · S = 0 and S · R(ξ,X) = 0. We prove that on a Lorentzian para-Sasakian manifold (M, φ, ξ, η, 1), if the Ricci curvature satisfies one of the previous conditions, the existence of η-Ricci solitons implies that (M, 1) is Einstein manifold. We also conclude that in these cases there is no Ricci soliton on M with the potential vector field ξ. On the other way, if M is of constant curvature, then (M, 1) is elliptic manifold. Cases when the Ricci tensor satisfies different other conditions are also discussed.

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