The Dirac spectrum on manifolds with gradient conformal vector fields

Details The Dirac spectrum on manifolds with gradient conformal vector fields The Dirac spectrum on manifolds with gradient conformal vector fields

2007-01-23

arxiv.org/abs/math/0701635v2

Journal of Functional Analysis 253, 1 (2007) 207-219

Mathematics

Differential Geometry

12 pages

Scientific paper

10.1016/j.jfa.2007.04.013

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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