Abstract
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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El Chami, F., Ginoux, N., Habib, G. et al. Rigidity results for spin manifolds with foliated boundary. J. Geom. 107, 533–555 (2016). https://doi.org/10.1007/s00022-015-0286-y
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DOI: https://doi.org/10.1007/s00022-015-0286-y