关于梯度Yamabe孤立子的平凡性结果  

Triviality results of gradient Yamabe solitons

作　　者：高梦敏 刘建成 GAO Mengmin;LIU Jiancheng(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,China)

机构地区：[1]西北师范大学数学与统计学院,甘肃兰州730070

出　　处：《湖北大学学报（自然科学版）》2024年第3期420-423,共4页Journal of Hubei University：Natural Science

基　　金：国家自然科学基金(12161078,11761061)资助。

摘　　要：研究完备非紧梯度Yamabe孤立子,在势函数梯度模长在无穷远处极限为0,或孤立子具有多项式体积增长,或孤立子随机完备的假设下,得到该类梯度Yamabe孤立子的平凡性结果,进而证得其数量曲率为常数。We studied the complete noncompact gradient Yamabe solitons,under certain assumptions such as the modulus of the gradient of potential function converging to zero at infinity,or the soliton having polynomial volume growth,or the soliton being stochastic complete,we obtained the triviality results,and proved that such solitons must have constant scalar curvature.

关 键 词：梯度Yamabe孤立子 常数量曲率 多项式体积增长 随机完备 

分 类 号：O186.12[理学—数学]