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The Dirac spectrum on manifolds with gradient conformal vector fields

Andrei Moroianu·Sergiu Moroianu
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Abstract

We show that the Dirac operator on a spin manifold does not admit $L^2$ eigenspinors provided the metric has a certain asymptotic behaviour and is a warped product near infinity. These conditions on the metric are fulfilled in particular if the manifold is complete and carries a non-complete vector field which outside a compact set is gradient conformal and non-vanishing.

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BibTeXRIS

Andrei Moroianu, Sergiu Moroianu. 2007-01-23. The Dirac spectrum on manifolds with gradient conformal vector fields. https://doi.org/10.1016/j.jfa.2007.04.013

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