卷积型梯度Yamabe孤立子的平凡性

Triviality of warped product gradient Yamabe solitons

研究卷积型梯度Yamabe孤立子,在基流形紧致且卷积函数和基流形的数量曲率满足一定的积分条件下,得到卷积型梯度Yamabe孤立子的平凡性结果;对基流形非紧且至多二次体积增长的情形,得到了卷积型梯度Yamabe孤立子平凡性结果的一个充分条件.

The warped product gradient Yamabe solitons is discussed in this paper.Triviality results of the warped product gradient Yamabe solitons are obtained under the condition that the base manifolds are compact and the scalar curvature of base manifolds and warping function satisfy certain integral condition.For the case of base manifolds be noncompact and with at most quadratic volume growth,a sufficient condition for the triviality results of the warped product gradient Yamabe solitons is obtained.