Let M be a connected compact C∞ manifold of dimension n≥4 without boundary. Let Mk be the set of all Ck Riemannian metrics on M. Any g∈Mk determines the Weyl tensor Wg:M→R4n,Wg(ξ):=(Wgijkl(ξ))i,j,k,l=1,…,n. We prove that the set A:=-g∈Mk:|Wg(ξ)|+|DWg(ξ)|+|D2Wg(ξ)|>0 for any ξ∈M} is an open dense subset of M k .
A generic result on weyl tensor / Micheletti, A. M.; Pistoia, A.. - In: TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS. - ISSN 1230-3429. - 53:1(2019), pp. 257-269. [10.12775/TMNA.2018.046]
A generic result on weyl tensor
Micheletti A. M.;Pistoia A.
2019
Abstract
Let M be a connected compact C∞ manifold of dimension n≥4 without boundary. Let Mk be the set of all Ck Riemannian metrics on M. Any g∈Mk determines the Weyl tensor Wg:M→R4n,Wg(ξ):=(Wgijkl(ξ))i,j,k,l=1,…,n. We prove that the set A:=-g∈Mk:|Wg(ξ)|+|DWg(ξ)|+|D2Wg(ξ)|>0 for any ξ∈M} is an open dense subset of M k .File allegati a questo prodotto
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