Residue Family Operators on Spinors and Spectral Theory of Dirac\n operator on Poincar 'e-Einstein Spaces

2014/02/03 by Matthias Fischmann, Fischmann, Matthias, Petr Somberg +1
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Advanced Operator Algebra Research #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Physics (math-ph) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1402.0336

openalex publication_date 2014/02/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study conformal Spin-subgeometry of submanifolds in a semi-Riemannian\nSpin-manifold, focusing on conformal Spin-manifolds (M,[h]) and their\nPoincar 'e-Einstein metrics (X,g₊). Our approach is based on the spectral\ntheory of Dirac operator in the ambient Spin-manifold, and associated spinor\nvalued meromorphic family of distributions with residues given by the residue\nfamily operators slashedD_N^res(h;\λ) on spinors. We develop basic\naspects and properties of slashedD_N^res(h;\λ) including conformal\ncovariance, factorization properties by conformally covariant operators for\nboth flat and curved semi-Riemannian Spin-manifolds, and Poisson\ntransformation.\n

Citations

• Conformally invariant powers of the ambient Dirac operator
• Generalized cylinders in semi-Riemannian and spin geometry

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