Rigidity results for Riemannian spin^c manifolds with foliated boundaryReport as inadecuate

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1 Université Libanaise 2 Géométrie IECL - Institut Élie Cartan de Lorraine 3 Notre Dame University-Louaize

Abstract : 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.

Keywords : Manifolds with boundary spin^c structures Riemannian flows Basic Dirac equation Kähler-Einstein manifolds parallel spinors

Author: Fida Chami - Nicolas Ginoux - Georges Habib - Roger Nakad -

Source: https://hal.archives-ouvertes.fr/


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