Triviality results for compact k-Yamabe solitons

Triviality results for quasi $k$-Yamabe solitons

“…Note that when m → ∞, then Theorem 1.3 correspond to Theorem 1.3 of [23]. On the other hand, combining Theorem 1.2 and Theorem 1.3, we have the following result.…”

“…It is worth noting that quasi k-Yamabe solitons correspond to a large class of manifolds well studied in the literature. 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].…”

“…Bo et al [4] also proved that any compact gradient k-Yamabe soliton with negative constant scalar curvature necessarily has constant σ k -curvature. In [23] it was shown that any compact gradient k-Yamabe soliton must be trivial. For m = ∞, Huang and Li [16] proved that any compact quasi 1-Yamabe gradient soliton is trivial.…”

“…which provides equation (22). For i = j, substituting ( 26) and ( 27) into (28) we obtain (23). Now, we need to consider the case α k0 = 1, α k = 0 for k = k 0 .…”