Rigidity Characterizations of Conformal Solitons

Junsheng Gong and Jiancheng Liu ()
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Junsheng Gong: College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China
Jiancheng Liu: College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

Mathematics, 2025, vol. 13, issue 11, 1-12

Abstract: 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.

Keywords: conformal soliton; gradient conformal soliton; p-harmonic map; classification (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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