A new upper bound for the Dirac operator on hypersurfaces
Differential Geometry
2016-01-20 v1 Spectral Theory
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 Schr\"odinger 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.
Cite
@article{arxiv.1402.1049,
title = {A new upper bound for the Dirac operator on hypersurfaces},
author = {Nicolas Ginoux and Georges Habib and Simon Raulot},
journal= {arXiv preprint arXiv:1402.1049},
year = {2016}
}