A rigidity theorem for complete noncompact Bach-flat manifolds

作者：Chu Yawei^*

来源：Journal of Geometry and Physics, 2011, 61(2): 516-521.

DOI：10.1016/j.geomphys.2010.11.003

• Bach-flat
• Rigidity
• Trace-free curvature tensor
• Space form

Let (M(4), g) be a four-dimensional complete noncompact Bach-flat Riemannian manifold with positive Yamabe constant. In this paper, we show that (M(4), g) has a constant curvature if it has a nonnegative constant scalar curvature and sufficiently small L(2)-norm of trace-free Riemannian curvature tensor. Moreover, we get a gap theorem for (M(4), g) with positive scalar curvature.

• 出版日期2011-2
• 单位郑州大学