On the eigenvalues of the twisted Dirac operator

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dc.creatorLeão, Marcos Jardim Rafael F.
dc.date2008-07-04
dc.date.accessioned2026-07-07T09:48:40Z
dc.date.available2026-07-07T09:48:40Z
dc.descriptionGiven a compact Riemannian spin manifold with positive scalar curvature, we find a family of connections $\nabla^{A_t}$ for $t\in[0,1]$ on a trivial vector bundle of sufficiently high rank, such that the first eigenvalue of the twisted Dirac operator $D_{A_t}$ is nonzero and becomes arbitrarily small as $t\to1$. 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.
dc.identifierhttps://arxiv.org/abs/0807.0813
dc.identifierhttp://arxiv.org/abs/0807.0813
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/164299
dc.subjectDifferential Geometry
dc.subjectMathematical Physics
dc.subject34L15
dc.titleOn the eigenvalues of the twisted Dirac operator
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