14,434 research outputs found
(1,1)-forms acting on Spinors on K\"ahler Surfaces
It is known that, for Dirac operators on Riemann surfaces twisted by line
bundles with Hermitian-Einstein connections, it is possible to obtain estimates
for the first eigenvalue in terms of the topology of the twisting bundle
\cite{JL2}. Attempts to generalize topological estimates for higher rank
bundles or higher dimensional manifolds have been so far unsuccessful. In this
work we construct a class of examples which indicates one problem that arises
on such attempts to derive topological estimates
On the spectrum of the twisted Dolbeault Laplacian over K\"ahler manifolds
We use Dirac operator techniques to a establish sharp lower bound for the
first eigenvalue of the Dolbeault Laplacian twisted by Hermitian-Einstein
connections on vector bundles of negative degree over compact K\"ahler
manifolds.Comment: 14 pages. Completely revised: estimates corrected and shown to be
shar
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