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This article is cited in 8 scientific papers (total in 8 papers)
Branson's $Q$-curvature in Riemannian and Spin Geometry
Oussama Hijazi, Simon Raulot Institut Élie Cartan Nancy, Nancy-Université, CNRS, INRIA, Boulevard des Aiguillettes B.P. 239 F-54506 Vandoeuvre-lès-Nancy Cedex, France
Abstract:
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.
Received: August 25, 2007; in final form November 29, 2007; Published online December 11, 2007
Citation:
Oussama Hijazi, Simon Raulot, “Branson's $Q$-curvature in Riemannian and Spin Geometry”, SIGMA, 3 (2007), 119, 11 pp.
Linking options:
https://www.mathnet.ru/eng/sigma245 https://www.mathnet.ru/eng/sigma/v3/p119
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Abstract page: | 229 | Full-text PDF : | 52 | References: | 36 |
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