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

Xiang Gao

doi:10.2478/auom-2013-0027

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

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Volume 21 (2013): Issue 2 (June 2013)

By: Xiang Gao

Open Access

|Sep 2013

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.

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