关于梯度Yamabe孤立子的平凡性结果

Triviality results of gradient Yamabe solitons

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.