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December 2005 A gap theorem for complete four-dimensional manifolds with $\deltaW^{+} = 0$
Takashi Okayasu
Tsukuba J. Math. 29(2): 539-542 (December 2005). DOI: 10.21099/tkbjm/1496164970

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 $W^{+}\equiv 0$.

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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

Information

Published: December 2005
First available in Project Euclid: 30 May 2017

zbMATH: 1094.53028
MathSciNet: MR2177026
Digital Object Identifier: 10.21099/tkbjm/1496164970

Rights: Copyright © 2005 University of Tsukuba, Institute of Mathematics

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Vol.29 • No. 2 • December 2005
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