On almost ∗-Ricci soliton

S. Kundu, S. Halder, K. De
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Abstract

Abstract. In the present paper, we prove three fundamental results concerning almost ∗-Ricci soliton in the framework of para-Sasakian manifold. The paper is organised as follows:• If a para-Sasakian metric g represents an almost ∗-Ricci soliton with potential vector field V is Jacobi along Reeb vector field ξ, then g becomes a ∗-Ricci soliton.• If a para-Sasakian metric g represents an almost ∗-Ricci soliton with potential vector field V as infinitesimal paracontact transformation, then V is killing and g is η-Einstein.• If a para-Sasakian metric g represents an almost ∗-Ricci soliton with potential vector field V is collinear with the Reeb vector field ξ, then λ = 0, V is strict and g is η-Einstein.
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关于几乎* -里奇孤子
摘要在拟sasakian流形的框架中,我们证明了关于几乎* -Ricci孤子的三个基本结果。•如果一个拟sasakian度规g表示一个几乎∗-Ricci孤子,其势向量场V沿Reeb向量场ξ为Jacobi,则g成为一个∗-Ricci孤子。•如果一个准sasakian度规g表示一个具有势向量场V的几乎* -Ricci孤子为无限小的准接触变换,则V是杀戮,g是η-爱因斯坦。•如果一个准sasakian度规g表示一个具有势向量场V与Reeb向量场ξ共线的几乎* -Ricci孤子,则λ = 0, V是严格的,g是η-Einstein。
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