Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

HOME ALL ARTICLES View

Bull. Korean Math. Soc. 2018; 55(3): 851-863

Online first article March 13, 2018      Printed May 31, 2018

https://doi.org/10.4134/BKMS.b170306

Copyright © The Korean Mathematical Society.

On a class of complete non-compact gradient Yamabe solitons

Jia-Yong Wu

Shanghai Maritime University

Abstract

We derive lower bounds of the scalar curvature on complete non-compact gradient Yamabe solitons under some integral curvature conditions. Based on this, we prove that potential functions of Yamabe solitons have at most quadratic growth for distance function. We also obtain a finite topological type property on complete shrinking gradient Yamabe solitons under suitable scalar curvature assumptions.

Keywords: Yamabe flow, Yamabe soliton, self-similar solution, finite topological type

MSC numbers: Primary 53C21; Secondary 53C44, 55Q52