Dirac Operator on Embedded Hypersurfaces

2000/12/29 by Oussama Hijazi, Sebastian Montiel, Hijazi, Oussama +4 · 1 citation
Mathematics · Physics and Astronomy · #53C27 #53C40 #53C80 #58G25 #Algebraic and Geometric Analysis #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Holomorphic and Operator Theory #Mathematical Physics (math-ph) #math-ph #math.DG #math.MP #msc:53C27 #msc:53C40 #msc:53C80 #msc:58G25

paper · pdf · doi:10.48550/arxiv.math/0012262

16 pages, LaTex, to appear in Math. Res. Letters

arxiv created 2000/12/29 · openalex publication_date 2000/12/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

New extrinsic lower bounds are given for the classical Dirac operator on the boundary of a compact domain of a spin manifold. The main tool is to solve some boundary problems for the Dirac operator of the domain under boundary conditions of Atiyah-Patodi-Singer type. Spinorial techniques are used to give simple proofs of classical results for compact embedded hypersurfaces.

Cited by

• Hypersurfaces immersed in special Spin^c manifolds by first eigenspinors

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