Rigidity of noncompact complete Bach-flat manifolds |
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Authors: | Seongtag Kim |
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Institution: | Department of Mathematics Education, Inha University, Incheon, 402-751, Republic of Korea |
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Abstract: | 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 L2 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 L2 bound of curvature tensor and L4/3 bound of scalar curvature. |
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Keywords: | 53c21 58c40 |
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