A new upper bound for the Dirac operator on hypersurfaces

Abstract

We prove a new upper bound for the first eigenvalue of the Dirac operator of a compact hypersurface in any Riemannian spin manifold carrying a non-trivial twistor spinor without zeros on the hypersurface. The upper bound is expressed as the first eigenvalue of a drifting Schrödinger operator on the hypersurface. Moreover, using a recent approach developed by O. Hijazi and S. Montiel, we completely characterize the equality case when the ambient manifold is the standard hyperbolic space.

References in corpus (2)

• Generalized Cylinders in Semi-Riemannian and Spin Geometry
• The supremum of conformally covariant eigenvalues in a conformal class

Cited by in corpus (1)

• Construction of initial data sets for Lorentzian manifolds with lightlike parallel spinors