arXiv:1310.3766 Abstract | arXiv Analytics

arXiv:1310.3766 [math.DG]Abstract References Reviews Resources

(1,1)-forms acting on Spinors on Kähler Surfaces

Published 2013-10-14Version 1

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.

Categories: math.DG

Subjects: 58Jxx

Keywords: kähler surfaces, higher rank bundles, higher dimensional manifolds, first eigenvalue, dirac operators

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