The Dirac spectrum on manifolds with gradient conformal vector fields

Andrei Moroianu (1) , Sergiu Moroianu (2)

1 CMLS - Centre de Mathématiques Laurent Schwartz
2 IMAR - Institutul de Matematica al Academiei Romane

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.

Mots clés: Dirac operator; hyperbolic manifolds; gradient conformal vector fields; continuous spectrum

Domaines: Géométrie différentielle [math.DG]

Andrei Moroianu, Sergiu Moroianu. The Dirac spectrum on manifolds with gradient conformal vector fields. Journal of Functional Analysis, 2007, 253 (1), pp.207-219. ⟨10.1016/j.jfa.2007.04.013⟩. ⟨hal-00125939v2⟩