Rigidity of noncompact complete Bach-flat manifolds

Details Rigidity of noncompact complete Bach-flat manifolds Rigidity of noncompact complete Bach-flat manifolds

2010-01-15

arxiv.org/abs/1001.2759v1

J. Geometry and Physics, 2010, Vol 60, p 637-642

Mathematics

Differential Geometry

10 pages, To appear J. Geom. Physics

Scientific paper

10.1016/j.geomphys.2009.12.014

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.

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