A holographic principle for the existence of imaginary Killing spinors
| Autor: | Sebastián Montiel, Oussama Hijazi, Simon Raulot |
|---|---|
| Přispěvatelé: | Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Universidad de Granada (UGR), Laboratoire de Mathématiques Raphaël Salem (LMRS), Université de Rouen Normandie (UNIROUEN), Normandie Université (NU)-Normandie Université (NU)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: |
Mathematics - Differential Geometry
Positive Mass Theorem Imaginary Killing spinors General Physics and Astronomy Dirac Operator Dirac operator 01 natural sciences symbols.namesake [MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM] Quantum mechanics 0103 physical sciences FOS: Mathematics Immersion (mathematics) 0101 mathematics Mathematical Physics Mathematics Mathematical physics Spinor Mean curvature Differential Geometry Global Analysis 53C27 53C40 53C80 58G25 010308 nuclear & particles physics Hyperbolic space 010102 general mathematics Asymptotically Hyperbolic manifolds Manifolds with Boundary 16. Peace & justice Differential Geometry (math.DG) [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG] Isospin Killing spinor Rigidity symbols Geometry and Topology Mathematics::Differential Geometry Scalar curvature |
| Zdroj: | Journal of Geometry and Physics Journal of Geometry and Physics, Elsevier, 2015, 91, pp.12-28. ⟨10.1016/j.geomphys.2015.01.012⟩ |
| ISSN: | 0393-0440 |
| DOI: | 10.1016/j.geomphys.2015.01.012⟩ |
| Popis: | Suppose that $\Sigma=\partial\Omega$ is the $n$-dimensional boundary, with positive (inward) mean curvature $H$, of a connected compact $(n+1)$-dimensional Riemannian spin manifold $(\Omega^{n+1},g)$ whose scalar curvature $R\ge -n(n+1)k^2$, for some $k\textgreater{}0$. If $\Sigma$ admits an isometric and isospin immersion $F$ into the hyperbolic space ${\mathbb{H}^{n+1}\_{-k^2}}$, we define a quasi-local mass and prove its positivity as well as the associated rigidity statement. The proof is based on a holographic principle for the existence of an imaginary Killing spinor. For $n=2$, we also show that its limit, for coordinate spheres in an Asymptotically Hyperbolic (AH) manifold, is the mass of the (AH) manifold. Comment: in Journal of Geometry and Physics, Elsevier, 2015 |
| Databáze: | OpenAIRE |
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