Yamabe constant evolution and monotonicity along the conformal Ricci flow

AIMS Mathematics

article

Yanlin Li¹  Abimbola Abolarinwa²  Shahroud Azami³  Akram Ali⁴ 

[1] School of Mathematics, Hangzhou Normal University;Department of Mathematics, University of Lagos;Department of pure Mathematics, Faculty of Science, Imam Khomeini International University;Department of Mathematics, College of Science, King Khalid University

关键词: Yamabe constant;    conformal Ricci flow;    Einstein metric;    scalar curvature;   

DOI  :  10.3934/math.2022671

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

We investigate the Yamabe constant's behaviour in a conformal Ricci flow. For conformal Ricci flow metric $ g(t) $, $ t \in [0, T) $, the time evolution formula for the Yamabe constant $ Y(g(t)) $ is derived. It is demonstrated that if the beginning metric $ g(0) = g_0 $ is Yamabe metric, then the Yamabe constant is monotonically growing along the conformal Ricci flow under some simple assumptions unless $ g_0 $ is Einstein. As a result, this study adds to the body of knowledge about the Yamabe problem.

【 授权许可】

CC BY