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Bull. Korean Math. Soc. 2023; 60(3): 623-636

Online first article May 11, 2023      Printed May 31, 2023

https://doi.org/10.4134/BKMS.b210927

Copyright © The Korean Mathematical Society.

Vanishing theorems for weighted harmonic $1$-forms on smooth metric measure spaces

Xiaoli Chao, Weili Wang

Southeast University; The Affiliated High School of Shenzhen University

Abstract

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In this paper, we prove some vanishing theorems under the assumptions of weighted BiRic curvature or $m$-Bakry-\'{E}mery-Ricci curvature bounded from below.

Keywords: Smooth metric measure spaces, weighted BiRic curvature, $m$-Bakry-\'{E}mery-Ricci curvature, $f$-minimal, harmonic form

MSC numbers: 53C24, 53C42

Supported by: This work is partially supported by the Natural Science Foundation of Jiangsu Province BK20161412.

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