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Article Dans Une Revue Journal of Geometry Année : 2016

Rigidity results for spin manifolds with foliated boundary

Résumé

In this paper, we consider a compact Riemannian manifold whose boundary is endowed with a Riemannian flow. Under a suitable curvature assumption depending on the O'Neill tensor of the flow, we prove that any solution of the basic Dirac equation is the restriction of a parallel spinor field defined on the whole manifold. As a consequence, we show that the flow is a local product. In particular, in the case where solutions of the basic Dirac equation are given by basic Killing spinors, we characterize the geometry of the manifold and the flow.
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Dates et versions

hal-01265987 , version 1 (01-02-2016)

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Fida El Chami, Nicolas Ginoux, Georges Habib, Roger Nakad. Rigidity results for spin manifolds with foliated boundary. Journal of Geometry, 2016, 107 (3), pp.533-555. ⟨10.1007/s00022-015-0286-y⟩. ⟨hal-01265987⟩
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