Methods and Applications of Analysis

Volume 21 (2014)

Number 3

Special issue dedicated to the 60th birthday of Stephen S.-T. Yau: Part I

Guest editors: John Erik Fornæss, Norwegian University of Science and Technology; Xiaojun Huang, Rutgers University; Song-Ying Li, University of California, Irvine; Yat Sun Poon, University of California, Riverside; Wing Shing Wong, The Chinese University of Hong Kong; and Zhouping Xin, The Institute of Mathematical Sciences, CUHK.

On a classification of the quasi Yamabe gradient solitons

Pages: 379 – 390

DOI: https://dx.doi.org/10.4310/MAA.2014.v21.n3.a7

Authors

Guangyue Huang (Department of Mathematics, Henan Normal University, Xinxiang, China)

Haizhong Li (Department of Mathematical Sciences, Tsinghua University, Beijing, China)

Abstract

In this paper, we introduce the concept of quasi Yamabe gradient solitons, which generalizes the concept of Yamabe gradient solitons. By using some ideas in [7, 8], we prove that $n$-dimensional ($n \geq 3$) complete quasi Yamabe gradient solitons with vanishing Weyl curvature tensor and positive sectional curvature must be rotationally symmetric. We also prove that any compact quasi Yamabe gradient solitons are of constant scalar curvature.

Keywords

locally conformally flat, quasi Yamabe gradient solitons, Weyl curvature tensor

2010 Mathematics Subject Classification

53C21, 53C25

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Published 8 October 2014