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2019 A generic result on Weyl tensor
Anna Maria Micheletti, Angela Pistoia
Topol. Methods Nonlinear Anal. 53(1): 257-269 (2019). DOI: 10.12775/TMNA.2018.046

Abstract

Let $M$ be a connected compact $C^\infty$ manifold of dimension $n\ge4$ without boundary. Let $ \mathcal{M}^k$ be the set of all $C^k$ Riemannian metrics on $M$. Any $g\in\mathcal{M}^k$ determines the Weyl tensor $$ \mathcal W^g\colon M\to \mathbb R^{4n},\qquad \mathcal W^g(\xi):=(W^g_{ijkl}(\xi))_{i,j,k,l=1,\dots,n}.$$ We prove that the set $$\mathcal{A}:=\big\{g\in \mathcal{M}^k : |\mathcal W^g(\xi)|+|D \mathcal W^g(\xi)|+|D^2 \mathcal W^g(\xi)|>0\ \hbox{for any}\ \xi\in M\big\}$$ is an open dense subset of $\mathcal{M}^k$.

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Anna Maria Micheletti. Angela Pistoia. "A generic result on Weyl tensor." Topol. Methods Nonlinear Anal. 53 (1) 257 - 269, 2019. https://doi.org/10.12775/TMNA.2018.046

Information

Published: 2019
First available in Project Euclid: 12 March 2019

zbMATH: 07068336
MathSciNet: MR3939155
Digital Object Identifier: 10.12775/TMNA.2018.046

Rights: Copyright © 2019 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.53 • No. 1 • 2019
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