Rigidity of noncompact complete Bach-flat manifolds

JOURNAL OF GEOMETRY AND PHYSICS

卷:60

Article

Kim, Seongtag

关键词: Bach-flat;    Einstein metric;    Conformally flat;    Weyl curvature;    Yamabe problem;   

DOI  :  10.1016/j.geomphys.2009.12.014

来源: Elsevier

【 摘 要 】

Let (M, g) be a noncompact complete Bach-flat manifold with positive Yamabe constant. We prove that (M, g) is flat if (M, g) has zero scalar curvature and sufficiently small L(2) bound of curvature tensor. When (M, g) has nonconstant scalar curvature, we prove that (M, g) is conformal to the flat space if (M, g) has sufficiently small L(2) bound of curvature tensor and L(4/3) bound of scalar curvature. (C) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

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