Geodesic
Branson's $Q$-curvature in Riemannian and Spin Geometry
Symmetry, integrability and geometry: methods and applications, Tome 3 (2007) Cet article a éte moissonné depuis la source Math-Net.Ru

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On a closed $n$-dimensional manifold, $n\ge 5$, we compare the three basic conformally covariant operators: the Paneitz–Branson, the Yamabe and the Dirac operator (if the manifold is spin) through their first eigenvalues. On a closed 4-dimensional Riemannian manifold, we give a lower bound for the square of the first eigenvalue of the Yamabe operator in terms of the total Branson's $Q$-curvature. As a consequence, if the manifold is spin, we relate the first eigenvalue of the Dirac operator to the total Branson's $Q$-curvature. Equality cases are also characterized.
Keywords: Branson's $Q$-curvature; eigenvalues; Yamabe operator; Paneitz–Branson operator; Dirac operator; $\sigma_k$-curvatures; Yamabe invariant; conformal geometry; Killing spinors. 
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     author = {Oussama Hijazi and Simon Raulot},
     title = {Branson's $Q$-curvature in {Riemannian} and {Spin} {Geometry}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2007},
     volume = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a118/}
}
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Oussama Hijazi; Simon Raulot. Branson's $Q$-curvature in Riemannian and Spin Geometry. Symmetry, integrability and geometry: methods and applications, Tome 3 (2007). http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a118/

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