Eigenvalue Estimates of the spinc Dirac Operator and Harmonic Forms on Kähler-Einstein Manifolds

• Veröffentlicht in: Symmetry, Integrability and Geometry: Methods and Applications
• Datum: 2015
• ISSN: 1815-0659
• Hauptverfasser: Nakad, R., Pilca, M.
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут математики НАН України 2015
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/147124
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: 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.

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.