Eigenvalue Estimates of the ${\rm spin}^c$ Dirac Operator and Harmonic Forms on K\"ahler-Einstein Manifolds
Differential Geometry
2015-07-15 v2
Abstract
We establish a lower bound for the eigenvalues of the Dirac operator defined on a compact K\"ahler-Einstein manifold of positive scalar curvature and endowed with particular structures. The limiting case is characterized by the existence of K\"ahlerian Killing spinors in a certain subbundle of the spinor bundle. Moreover, we show that the Clifford multiplication between an effective harmonic form and a K\"ahlerian Killing spinor field vanishes. This extends to the case the result of A. Moroianu stating that, on a compact K\"ahler-Einstein manifold of complex dimension carrying a complex contact structure, the Clifford multiplication between an effective harmonic form and a K\"ahlerian Killing spinor is zero.
Keywords
Cite
@article{arxiv.1502.05252,
title = {Eigenvalue Estimates of the ${\rm spin}^c$ Dirac Operator and Harmonic Forms on K\"ahler-Einstein Manifolds},
author = {Roger Nakad and Mihaela Pilca},
journal= {arXiv preprint arXiv:1502.05252},
year = {2015}
}