关于完备收缩的Ricci-harmonic孤子的研究（英文）  

ON COMLETE SHRINKING RICCI-HARMONIC SOLITONS

作　　者：杨飞[1] 张良迪 

机构地区：[1]中国地质大学(武汉)数学与物理学院,湖北武汉430063

出　　处：《数学杂志》2016年第3期494-500,共7页Journal of Mathematics

基　　金：Supported by Tian Yuan Special Funds of the National Natural Science Foundation of China(11326076)

摘　　要：本文研究了收缩的Ricci-harmonic孤子的几何性质的问题.利用文献[4]在Ricci孤子下的方法,获得了每个紧致Ricci-harmonic孤子是一个梯度孤子的结论,推广了Perelman等人在Ricci孤子下的结果.此外,利用文献[14]在Ricci孤子下的方法,获得了完备非紧梯度收缩的Ricci-harmonic孤子具有比至多欧氏增长更加精确的体积增长估计的结果,推广了文献[14]在Ricci孤子下的结果.In this paper,we study the geometry of shrinking Ricci-harmonic solitons.By utilizing the method of Manola,Gabriele and Carlo[4]under the Ricci soliton,we prove the result that every compact shrinking Ricci-harmonic soliton is a gradient one,which extends the result in the case of Ricci solition.Moreover,by utilizing the method of Zhang[14],we prove a more precise volume growth estimate than that of at most Euclidean growth for the complete non-compact gradient shrinking Ricci-harmonic soliton,which extends the result of Zhang[14]in the case of Ricci solition.

关 键 词：收缩的Ricci-harmonic孤子 梯度 体积增长 

分 类 号：O186.12[理学—数学]