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6 papers · 2 filters
Flat nearly Kähler manifolds
Vicente Cortés, Lars Schäfer
We classify flat strict nearly Kähler manifolds with (necessarily) indefinite metric. Any such manifold is locally the product of a flat pseudo-Kähler factor of maximal dimension a…
The first eigenvalue of Dirac and Laplace operators on surfaces
Jean-Francois Grosjean, Emmanuel Humbert
Let be a compact Riemmannian surface equipped with a spin structure . For any metric on , we denote by (resp. ) the f…
The spinorial τ-invariant and 0-dimensional surgery
Bernd Ammann, Emmanuel Humbert
Let be a compact manifold with a metric and with a fixed spin structure . Let be the first non-negative eigenvalue of the Dirac operator on . We set…
Surgery and Harmonic Spinors
Bernd Ammann, Mattias Dahl, Emmanuel Humbert
Let M be a compact manifold with a fixed spin structure χ. The Atiyah-Singer index theorem implies that for any metric g on M the dimension of the kernel of the Dirac operator is b…
The Hijazi inequality on manifolds with boundary
Simon Raulot
In this paper, we prove the Hijazi inequality on compact Riemannian spin manifolds under two boundary conditions: the condition associated with a chirality operator and the Riemann…
Extrinsic radius pinching for hypersurfaces of space forms
Julien Roth
We prove some pinching results for the extrinsic radius of compact hypersurfaces in space forms. We show that if the pinching condion is strong enough with a dependance on the norm…