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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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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