Rigidity Results for Riemannian Spin Manifolds with Foliated Boundary

被引：0

作者：

El Chami, Fida ^{[1
]}

Ginoux, Nicolas ^{[2
]}

Habib, Georges ^{[1
]}

Nakad, Roger ^{[3
]}

机构：

[1] Lebanese Univ, Dept Math, Fac Sci 2, POB 90656, Fanar Matn, Lebanon

[2] Univ Lorraine, Inst Elie Cartan Lorraine, Site Metz,Rue Augustin Fresnel, F-57070 Metz, France

[3] Notre Dame Univ Louaize, Fac Nat & Appl Sci, Dept Math & Stat, POB 72, Zouk Mikael, Lebanon

来源：

RESULTS IN MATHEMATICS | 2017年 / 72卷 / 04期

关键词：

Manifolds with boundary; spin(c) structures; Riemannian flows; basic Dirac equation; Kahler-Einstein manifolds; parallel spinors; REAL HYPERSURFACES; KILLING SPINORS; DIRAC; LAPLACIAN; OPERATORS; PARALLEL;

D O I：

10.1007/s00025-017-0734-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Given a Riemannian spin 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 Kahler-Einstein manifold or a Riemannian product of a Kahler-Einstein manifold with (or with the circle ).

引用

页码：1773 / 1806

页数：34

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