On the scalar curvature estimates for gradient Yamabe solitons

On warped product gradient Yamabe solitons

“…As noticed by Wu this result excludes the analysis of Einstein solitons with negative constant curvature. Observing such gap, Chu [11] improve this result by considering a lower bound of Bakry-Émery Ricci tensor.…”

“…Theorem 1.2. ( [11]) Let (M n , g, ∇h, ρ) be an n-dimensional complete noncompact gradient Yamabe soliton with…”

“…Next, again by (11), the weak minimum principle at infinity for ∆ w holds (see Theorem 9 of [42]). Then there exist a sequence {x k } such that,…”

Triviality results for quasi $k$-Yamabe solitons

“…For instance, if m → ∞, then quasi k-Yamabe solitons reduces to k-Yamabe solitons [2,4,8,23]. Also, since σ 1 = R 2(n−1) , 1-Yamabe solitons naturally correspond to Yamabe solitons [5,6,7,10,11,12,13,15,17,22], and quasi 1-Yamabe solitons correspond to quasi Yamabe solitons studied in [16,25]. When X = ∇f is a gradient vector field, quasi 1-Yamabe gradient solitons correspond to an f -almost Yamabe soliton [27].…”

A note on compact CR Yamabe solitons

“…Yamabe soliton has been studied by many authors. See [4,5,9,10,11,16,17,21,22] and the references therein. In particular, we mention the following theorem related to the main result in this paper, which was obtained independently by di Cerbo and Disconzi in [11] and by Hsu in [16]: Suppose (M, θ) is a strictly pseudoconvex CR manifold of real dimension 2n + 1.…”