Mathematics, Vol. 13, Pages 1837: Rigidity Characterizations of Conformal Solitons

Mathematics doi: 10.3390/math13111837

Authors:
Junsheng Gong
Jiancheng Liu

We study the rigidity of conformal solitons, give a sufficient and necessary condition that guarantees that every closed conformal soliton is gradient conformal soliton, and prove that complete conformal solitons with a nonpositive Ricci curvature must be trivial under an integral condition. In particular, by using a p-harmonic map from a complete gradient conformal soliton in a smooth Riemannian manifold, we classify complete noncompact nontrivial gradient conformal solitons under some suitable conditions, and similar results are given for gradient Yamabe solitons and gradient k-Yamabe solitons.

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Junsheng Gong www.mdpi.com