<abstract xmlns="http://www.w3.org/1999/xhtml"> In this paper, we deal with the complete non-compact expanding gradient Ricci soliton (Mn,g) with positive Ricci curvature. On the condition that the Ricci curvature is positive and the scalar curvature approaches 0 towards infinity, we derive a useful estimate on the growth of potential functions. Based on this and under the same assumptions, we prove that ∫t0 Rc (γ'(s) , γ' (s))ds and ∫t0 Rc (γ' (,s). v)ds at least have linear growth, where 7(5) is a minimal normal geodesic emanating from the point where R obtains its maximum. Furthermore, some other results on the Ricci curvature are also obtained. </abstract>

In this paper, we deal with the complete non-compact expanding gradient Ricci soliton (Mn,g) with positive Ricci curvature. On the condition that the Ricci curvature is positive and the scalar curvature approaches 0 towards infinity, we derive a useful estimate on the growth of potential functions. Based on this and under the same assumptions, we prove that ∫t0 Rc (γ'(s) , γ' (s))ds and ∫t0 Rc (γ' (,s). v)ds at least have linear growth, where 7(5) is a minimal normal geodesic emanating from the point where R obtains its maximum. Furthermore, some other results on the Ricci curvature are also obtained.

Estimates on the non-compact expanding gradient Ricci solitons

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

Institute of Science, Information Engineering University, Zhengzhou City, Henan Province, 450001, People’s Republic of China

School of Mathematical Sciences, Qingdao University, Lane 308, Ningxia Road, Shinan District, Qingdao City, Shandong Province, 266071, People’s Republic of China

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

{"article-title":"Estimates on the non-compact expanding gradient Ricci solitons"}

In this paper, we deal with the complete non-compact expanding gradient Ricci soliton (Mn,g) with positive Ricci curvature. On the condition that the Ricci...

Estimates on the non-compact expanding gradient Ricci solitons

Online veröffentlicht: 05. März 2014

Seitenbereich: 95 - 102

DOI: https://doi.org/10.2478/auom-2013-0046

Schlüsselwörter
Ricci ow, expanding gradient Ricci soliton, Ricci curvature

This content is open access.

Estimates on the non-compact expanding gradient Ricci solitons

Online veröffentlicht: 05. März 2014

Seitenbereich: 95 - 102

DOI: https://doi.org/10.2478/auom-2013-0046

SchlüsselwörterRicci ow, expanding gradient Ricci soliton, Ricci curvature

This content is open access.

Schlüsselwörter
Ricci ow, expanding gradient Ricci soliton, Ricci curvature