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Article Dans Une Revue Results in mathematics = Resultate der Mathematik Année : 2017

Rigidity results for Riemannian spin$^c$ manifolds with foliated boundary

Résumé

Given a Riemannian spin^c manifold whose boundary is endowed with a Riemannian flow, we show that any solution of the basic Dirac equation satisfies an integral inequality depending on geometric quantities, such as the mean curvature and the O'Neill tensor. We then characterize the equality case of the inequality when the ambient manifold is a domain of a Kähler-Einstein manifold or a Riemannian product of a Kähler-Einstein manifold with R (or with the circle S^1).
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Dates et versions

hal-01412760 , version 1 (08-12-2016)

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Fida El Chami, Nicolas Ginoux, Georges Habib, Roger Nakad. Rigidity results for Riemannian spin$^c$ manifolds with foliated boundary. Results in mathematics = Resultate der Mathematik, 2017, 72 (4), pp.1773-1806. ⟨10.1007/s00025-017-0734-0⟩. ⟨hal-01412760⟩
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