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Article Dans Une Revue Annals of Global Analysis and Geometry Année : 1999

Generalized Killing Spinors and Conformal Eigenvalue Estimates for Spin^c Manifolds

Résumé

In this paper we prove the Spin^c analog of the Hijazi inequality on the first eigenvalue of the Dirac operator on compact Riemannian manifolds and study its equality case. During this study, we are naturally led to consider generalized Killing spinors on Spin^c manifolds and we prove that such objects can only exist on low-dimensional manifolds (up to dimension three). This allows us to give a nice geometrical description of the manifolds satisfying the equality case of the above-mentioned inequality and to classify them in dimension three and four.
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Dates et versions

hal-00125994 , version 1 (23-01-2007)

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Marc Herzlich, Andrei Moroianu. Generalized Killing Spinors and Conformal Eigenvalue Estimates for Spin^c Manifolds. Annals of Global Analysis and Geometry, 1999, 17, pp.341-370. ⟨10.1023/A:1006546915261⟩. ⟨hal-00125994⟩
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