Zusammenfassung
We establish a lower bound for the eigenvalues of the Dirac operator defined on a compact Kahler-Einstein manifold of positive scalar curvature and endowed with particular spin(c) structures. The limiting case is characterized by the existence of Kahlerian Killing spin(c) spinors in a certain subbundle of the spinor bundle. Moreover, we show that the Clifford multiplication between an effective ...
Zusammenfassung
We establish a lower bound for the eigenvalues of the Dirac operator defined on a compact Kahler-Einstein manifold of positive scalar curvature and endowed with particular spin(c) structures. The limiting case is characterized by the existence of Kahlerian Killing spin(c) spinors in a certain subbundle of the spinor bundle. Moreover, we show that the Clifford multiplication between an effective harmonic form and a Kahlerian Killing spin(c) spinor field vanishes. This extends to the spin(c) case the result of A. Moroianu stating that, on a compact Kahler-Einstein manifold of complex dimension 4l + 3 carrying a complex contact structure, the Clifford multiplication between an effective harmonic form and a Kahlerian Killing spinor is zero.
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