We confirm the validity of a conjecture of Besse within the class of compact, regular, locally homogeneous contact metric manifolds, showing that such a manifold M must be isometric to the standard sphere S^{2n+1}, provided the scalar curvature equals 2n(2n + 1), where dim(M) = 2n+1, and the Riemannian metric associated to the contact form satisfies the critical point equation for the total scalar curvature functional.
On the Besse’s conjecture for compact regular contact metric manifolds
Lotta
In corso di stampa
Abstract
We confirm the validity of a conjecture of Besse within the class of compact, regular, locally homogeneous contact metric manifolds, showing that such a manifold M must be isometric to the standard sphere S^{2n+1}, provided the scalar curvature equals 2n(2n + 1), where dim(M) = 2n+1, and the Riemannian metric associated to the contact form satisfies the critical point equation for the total scalar curvature functional.File in questo prodotto:
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