Second Order Symmetries of the Conformal Laplacian
Let (M,g) be an arbitrary pseudo-Riemannian manifold of dimension at least 3. We determine the form of all the conformal symmetries of the conformal (or Yamabe) Laplacian on (M,g), which are given by differential operators of second order. They are constructed from conformal Killing 2-tensors satisf...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2014 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2014
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/146838 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Second Order Symmetries of the Conformal Laplacian / J.P. Michel, F. Radoux, J. Šilhan // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 31 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862583732520615936 |
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| author | Michel, J.P. Radoux, F. Šilhan, J. |
| author_facet | Michel, J.P. Radoux, F. Šilhan, J. |
| citation_txt | Second Order Symmetries of the Conformal Laplacian / J.P. Michel, F. Radoux, J. Šilhan // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 31 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Let (M,g) be an arbitrary pseudo-Riemannian manifold of dimension at least 3. We determine the form of all the conformal symmetries of the conformal (or Yamabe) Laplacian on (M,g), which are given by differential operators of second order. They are constructed from conformal Killing 2-tensors satisfying a natural and conformally invariant condition. As a consequence, we get also the classification of the second order symmetries of the conformal Laplacian. Our results generalize the ones of Eastwood and Carter, which hold on conformally flat and Einstein manifolds respectively. We illustrate our results on two families of examples in dimension three.
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| first_indexed | 2025-11-27T00:43:21Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-146838 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-27T00:43:21Z |
| publishDate | 2014 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Michel, J.P. Radoux, F. Šilhan, J. 2019-02-11T17:00:31Z 2019-02-11T17:00:31Z 2014 Second Order Symmetries of the Conformal Laplacian / J.P. Michel, F. Radoux, J. Šilhan // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 31 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 58J10; 53A30; 70S10; 53D20; 53D55 DOI:10.3842/SIGMA.2014.016 https://nasplib.isofts.kiev.ua/handle/123456789/146838 Let (M,g) be an arbitrary pseudo-Riemannian manifold of dimension at least 3. We determine the form of all the conformal symmetries of the conformal (or Yamabe) Laplacian on (M,g), which are given by differential operators of second order. They are constructed from conformal Killing 2-tensors satisfying a natural and conformally invariant condition. As a consequence, we get also the classification of the second order symmetries of the conformal Laplacian. Our results generalize the ones of Eastwood and Carter, which hold on conformally flat and Einstein manifolds respectively. We illustrate our results on two families of examples in dimension three. A special thanks is due to Jonathan Kress which points out a mistake in one of the example
 provided in the first version of this paper. It is a pleasure to acknowledge also Christian Duval
 and Galliano Valent for their constant interest in this work. Josef Silhan would like to thank ˇ
 Pawel Nurowski for helpful discussions.
 This research has been partially funded by the Interuniversity Attraction Poles Program
 initiated by the Belgian Science Policy Of fice. J. Silhan was supported by the grant agency of ˇ
 the Czech republic under the grant P201/12/G028. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Second Order Symmetries of the Conformal Laplacian Article published earlier |
| spellingShingle | Second Order Symmetries of the Conformal Laplacian Michel, J.P. Radoux, F. Šilhan, J. |
| title | Second Order Symmetries of the Conformal Laplacian |
| title_full | Second Order Symmetries of the Conformal Laplacian |
| title_fullStr | Second Order Symmetries of the Conformal Laplacian |
| title_full_unstemmed | Second Order Symmetries of the Conformal Laplacian |
| title_short | Second Order Symmetries of the Conformal Laplacian |
| title_sort | second order symmetries of the conformal laplacian |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146838 |
| work_keys_str_mv | AT micheljp secondordersymmetriesoftheconformallaplacian AT radouxf secondordersymmetriesoftheconformallaplacian AT silhanj secondordersymmetriesoftheconformallaplacian |