四维完备梯度近Ricci孤立子的局部特征

Local Characterization of Four-Dimensional Complete Gradient almost Ricci Solitons

用几何分析的方法,并结合一些重要不等式,研究满足特定条件(与Weyl张量的反自对偶或自对偶部分相关)的四维完备梯度近Ricci孤立子的局部特征,证得该孤立子在局部上是具有三维常截面曲率纤维的卷积结构或具有三维Einstein纤维的卷积结构.

By using the method of geometric analysis and some important inequalities,we studied the local characterization of four-dimensional complete gradient almost Ricci solitons satisfying certain conditions involving either the anti-self-dual or self-dual part of the Weyl tensor,and proved that such solitons were locally warped product structure with three-dimensional constant sectional curvature fibers or three-dimensional Einstein fibers.