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On the eigenvalues of the twisted Dirac operator
J. Math. Phys. 50, 063513 (2009); doi:10.1063/1.3133944
Published 24 June 2009
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Given a compact Riemannian spin manifold whose untwisted Dirac operator has trivial kernel, we find a family of connections ![[del]](http://scitation.aip.org/stockgif3/nabla.gif)
At for t![[is-an-element-of]](http://scitation.aip.org/stockgif3/isin.gif)
[0,1] on a trivial vector bundle of rank no larger than dim M+1, such that the first eigenvalue of the twisted Dirac operator DAt is nonzero for t![[not-equal]](http://scitation.aip.org/stockgif3/ne.gif)
1 and vanishes for t=1. However, if one restricts the class of twisting connections considered, then nonzero lower bounds do exist. We illustrate this fact by establishing a nonzero lower bound for the Dirac operator twisted by Hermitian–Einstein connections over Riemann surfaces.
©2009 American Institute of Physics
At for t[0,1] on a trivial vector bundle of rank no larger than dim M+1, such that the first eigenvalue of the twisted Dirac operator DAt is nonzero for t1 and vanishes for t=1. However, if one restricts the class of twisting connections considered, then nonzero lower bounds do exist. We illustrate this fact by establishing a nonzero lower bound for the Dirac operator twisted by Hermitian–Einstein connections over Riemann surfaces.
©2009 American Institute of Physics
| History: | Received 3 June 2008; accepted 22 April 2009; published 24 June 2009 |
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http://link.aip.org/link/?JMAPAQ/50/063513/1 |
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