Branson's Q-curvature in Riemannian and Spin Geometry
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...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2007 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2007
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/147214 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862656014082375680 |
|---|---|
| author | Hijazi, O. Raulot, S. |
| author_facet | Hijazi, O. Raulot, S. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2025-12-02T03:29:23Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147214 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-02T03:29:23Z |
| publishDate | 2007 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Hijazi, O. Raulot, S. 2019-02-13T19:10:41Z 2019-02-13T19:10:41Z 2007 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. 1815-0659 2000 Mathematics Subject Classification: 53C20; 53C27; 58J50 https://nasplib.isofts.kiev.ua/handle/123456789/147214 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. 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Branson's Q-curvature in Riemannian and Spin Geometry Article published earlier |
| spellingShingle | Branson's Q-curvature in Riemannian and Spin Geometry Hijazi, O. Raulot, S. |
| title | Branson's Q-curvature in Riemannian and Spin Geometry |
| title_full | Branson's Q-curvature in Riemannian and Spin Geometry |
| title_fullStr | Branson's Q-curvature in Riemannian and Spin Geometry |
| title_full_unstemmed | Branson's Q-curvature in Riemannian and Spin Geometry |
| title_short | Branson's Q-curvature in Riemannian and Spin Geometry |
| title_sort | branson's q-curvature in riemannian and spin geometry |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147214 |
| work_keys_str_mv | AT hijazio bransonsqcurvatureinriemannianandspingeometry AT raulots bransonsqcurvatureinriemannianandspingeometry |