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Branson's Q-curvature in Riemannian and Spin Geometry
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2007, том 3
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Branson's Q-curvature in Riemannian and Spin Geometry
Інший ID:
2000 Mathematics Subject Classification: 53C20; 53C27; 58J50
Посилання:
Branson's Q-curvature in Riemannian and Spin Geometry / O. Hijazi, S. Raulot // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 23 назв. — англ.
Підтримка:
This paper is a contribution to the Proceedings of the 2007 Midwest Geometry Conference in honor of Thomas P. Branson. We would like to thank the referees for their careful reading and suggestions.
Дата:
2007
Переглядів:
591
Завантажень:
256
Анотація:
On a closed n-dimensional manifold, n ≥ 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.
