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Eigenvalue Estimates of the spinc Dirac Operator and Harmonic Forms on Kähler-Einstein Manifolds
We establish a lower bound for the eigenvalues of the Dirac operator defined on a compact Kähler-Einstein manifold of positive scalar curvature and endowed with particular spinc structures. The limiting case is characterized by the existence of Kählerian Killing spinc spinors in a certain subbundle...
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Інститут математики НАН України
2015
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/147124 |
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irk-123456789-1471242019-02-14T01:23:45Z Eigenvalue Estimates of the spinc Dirac Operator and Harmonic Forms on Kähler-Einstein Manifolds Nakad, R. Pilca, M. We establish a lower bound for the eigenvalues of the Dirac operator defined on a compact Kähler-Einstein manifold of positive scalar curvature and endowed with particular spinc structures. The limiting case is characterized by the existence of Kählerian Killing spinc spinors in a certain subbundle of the spinor bundle. Moreover, we show that the Clifford multiplication between an effective harmonic form and a Kählerian Killing spinc spinor field vanishes. This extends to the spinc case the result of A. Moroianu stating that, on a compact Kähler-Einstein manifold of complex dimension 4ℓ+3 carrying a complex contact structure, the Clifford multiplication between an effective harmonic form and a Kählerian Killing spinor is zero. 2015 Article Eigenvalue Estimates of the spinc Dirac Operator and Harmonic Forms on Kähler-Einstein Manifolds / R. Nakad, M. Pilca // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 39 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 53C27; 53C25; 53C55; 58J50; 83C60 DOI:10.3842/SIGMA.2015.054 http://dspace.nbuv.gov.ua/handle/123456789/147124 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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English |
| description |
We establish a lower bound for the eigenvalues of the Dirac operator defined on a compact Kähler-Einstein manifold of positive scalar curvature and endowed with particular spinc structures. The limiting case is characterized by the existence of Kählerian Killing spinc spinors in a certain subbundle of the spinor bundle. Moreover, we show that the Clifford multiplication between an effective harmonic form and a Kählerian Killing spinc spinor field vanishes. This extends to the spinc case the result of A. Moroianu stating that, on a compact Kähler-Einstein manifold of complex dimension 4ℓ+3 carrying a complex contact structure, the Clifford multiplication between an effective harmonic form and a Kählerian Killing spinor is zero. |
| format |
Article |
| author |
Nakad, R. Pilca, M. |
| spellingShingle |
Nakad, R. Pilca, M. Eigenvalue Estimates of the spinc Dirac Operator and Harmonic Forms on Kähler-Einstein Manifolds Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Nakad, R. Pilca, M. |
| author_sort |
Nakad, R. |
| title |
Eigenvalue Estimates of the spinc Dirac Operator and Harmonic Forms on Kähler-Einstein Manifolds |
| title_short |
Eigenvalue Estimates of the spinc Dirac Operator and Harmonic Forms on Kähler-Einstein Manifolds |
| title_full |
Eigenvalue Estimates of the spinc Dirac Operator and Harmonic Forms on Kähler-Einstein Manifolds |
| title_fullStr |
Eigenvalue Estimates of the spinc Dirac Operator and Harmonic Forms on Kähler-Einstein Manifolds |
| title_full_unstemmed |
Eigenvalue Estimates of the spinc Dirac Operator and Harmonic Forms on Kähler-Einstein Manifolds |
| title_sort |
eigenvalue estimates of the spinc dirac operator and harmonic forms on kähler-einstein manifolds |
| publisher |
Інститут математики НАН України |
| publishDate |
2015 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147124 |
| citation_txt |
Eigenvalue Estimates of the spinc Dirac Operator and Harmonic Forms on Kähler-Einstein Manifolds / R. Nakad, M. Pilca // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 39 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT nakadr eigenvalueestimatesofthespincdiracoperatorandharmonicformsonkahlereinsteinmanifolds AT pilcam eigenvalueestimatesofthespincdiracoperatorandharmonicformsonkahlereinsteinmanifolds |
| first_indexed |
2023-05-20T17:26:38Z |
| last_indexed |
2023-05-20T17:26:38Z |
| _version_ |
1796153298552619008 |