<abstract xmlns="http://www.w3.org/1999/xhtml"> In this paper, we firstly establish a useful ODE relationship between R1(c) and V1(c) on the steady Ricci soliton. Based on this, we obtain a necessary and sufficient condition for some complete noncompact steady gradient Ricci solitons to have positive asymptotic volume ratio. </abstract>

In this paper, we firstly establish a useful ODE relationship between R1(c) and V1(c) on the steady Ricci soliton. Based on this, we obtain a necessary and sufficient condition for some complete noncompact steady gradient Ricci solitons to have positive asymptotic volume ratio.

A necessary and sufficient condition for some steady Ricci solitons to have positive asymptotic volume ratio

School of Mathematical Sciences, Ocean University of China, Lane 238, Songling Road, Laoshan District, Qingdao City, Shandong Province, 266100, People's Republic of China

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

In this paper, we firstly establish a useful ODE relationship between R1(c) and V1(c) on the steady Ricci soliton. Based on this, we obtain a necessary and...

A necessary and sufficient condition for some steady Ricci solitons to have positive asymptotic volume ratio

Published Online: Sep 19, 2013

Page range: 131 - 139

DOI: https://doi.org/10.2478/auom-2013-0027

Keywords
steady Ricci soliton, asymptotic volume ratio, potential function

This content is open access.

A necessary and sufficient condition for some steady Ricci solitons to have positive asymptotic volume ratio

Published Online: Sep 19, 2013

Page range: 131 - 139

DOI: https://doi.org/10.2478/auom-2013-0027

Keywordssteady Ricci soliton, asymptotic volume ratio, potential function

This content is open access.

Keywords
steady Ricci soliton, asymptotic volume ratio, potential function