A Note on Rigidity and Vanishing Theorems for Translating Solitons

Jiji Peng and Guangwen Zhao ()
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Jiji Peng: School of Mathematics and Statistics, Wuhan University of Technology, Wuhan 430070, China
Guangwen Zhao: School of Mathematics and Statistics, Wuhan University of Technology, Wuhan 430070, China

Mathematics, 2025, vol. 13, issue 14, 1-12

Abstract: In this short note, we focus on complete translating solitons with a bounded L f n -norm of the second fundamental form and obtain two results. First, based on a Sobolev-type inequality and a Simons-type inequality, we establish a rigidity theorem of complete translating solitons. Second, based on the same Sobolev-type inequality and a Bochner-type inequality, a vanishing theorem regarding L f p weighted harmonic 1-forms is proved.

Keywords: translating soliton; the second fundamental form; weighted harmonic 1-form (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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