Rigidity results for spin manifolds with foliated boundary
| Autor: | Georges Habib, Roger Nakad, Nicolas Ginoux, Fida El Chami |
|---|---|
| Přispěvatelé: | Université Libanaise, Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Notre Dame University-Louaize [Lebanon] (NDU), Lecturer at IUT de Metz |
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Mathematics - Differential Geometry
Riemann curvature tensor O'Neill tensor Basic Killing spinors 01 natural sciences Pseudo-Riemannian manifold 53C24 symbols.namesake special vector fields Mathematics Subject Classification: 53C27 0103 physical sciences FOS: Mathematics Hermitian manifold 0101 mathematics Ricci curvature Mathematics mean curva-ture Mean curvature flow Basic Dirac equation Curvature of Riemannian manifolds Manifolds with boundary second fundamental form 010102 general mathematics Mathematical analysis Holonomy 53C12 Differential Geometry (math.DG) [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG] Riemannian flows symbols 010307 mathematical physics Geometry and Topology Mathematics::Differential Geometry Scalar curvature |
| Zdroj: | Journal of Geometry Journal of Geometry, Springer Verlag, 2016, 107 (3), pp.533-555. ⟨10.1007/s00022-015-0286-y⟩ |
| ISSN: | 0047-2468 1420-8997 |
| Popis: | 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. Comment: 22 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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