The Dirac spectrum on manifolds with gradient conformal vector fields

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.

12 pages

References in corpus (2)

• Generalized Cylinders in Semi-Riemannian and Spin Geometry
• The spectrum of magnetic Schrödinger operators and $k$-form Laplacians on conformally cusp manifolds

Cited by in corpus (2)

• Spectral Bounds for Dirac Operators on Open Manifolds
• The Dirac operator on generalized Taub-NUT spaces