Abstract
Let $M^{4}$ be a complete noncompact oriented fourdimensional Riemannian manifold satisfying $\delta W^{+}=0$, where $W^{+}$ is the self-dual part of the Weyl curvature tensor. Suppose its scalar curvature is nonnegative and Sobolev's inequality holds. We show that if the $L^{2}$ norm of $W^{+}$ is sufficiently small, then $W^{+}\equiv 0$.
Citation
Takashi Okayasu. "A gap theorem for complete four-dimensional manifolds with $\deltaW^{+} = 0$." Tsukuba J. Math. 29 (2) 539 - 542, December 2005. https://doi.org/10.21099/tkbjm/1496164970
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