Ricci solitons on η-einstein contact manifolds

...Given the contact metric manifold (M, η, ξ, φ, 1), we have the following identities ([1], [2]): hξ = 0, hφ + φh = 0,...

...A (2n + 1)-dimensional manifold M is said to admit an almost contact structure if it admits a tensor field φ of type (1, 1), a vector field ξ and a 1-form η satisfying ([1],[2]) (a) φ2 = −I + η ⊗ ξ, (b) η(ξ) = 1, (c) φξ = 0, (d) η ◦ φ = 0....

...Given the contact metric manifold (M, η, ξ, φ, 1), we have the following identities ([1], [2]): hξ = 0, hφ + φh = 0,...

...A (2n + 1)-dimensional manifold M is said to admit an almost contact structure if it admits a tensor field φ of type (1, 1), a vector field ξ and a 1-form η satisfying ([1],[2]) (a) φ2 = −I + η ⊗ ξ, (b) η(ξ) = 1, (c) φξ = 0, (d) η ◦ φ = 0....

...There exist many non-trivial examples of Ricci solitons compact as well as non-compact ([15],[26], [27])....

...For details we refer to Chow and Knoff [15]....

...A Riemannian manifold is called locally symmetric [16] if ∇R = 0, where R is the Riemannian curvature tensor of (Mn, 1)....