On Conformal Powers of the Dirac Operator on Einstein Manifolds
Differential Geometry
2021-06-01 v1 Mathematical Physics
Analysis of PDEs
Combinatorics
math.MP
Abstract
We determine the structure of conformal powers of the Dirac operator on Einstein {\it Spin}-manifolds in terms of the product formula for shifted Dirac operators. The result is based on the techniques of higher variations for the Dirac operator on Einstein manifolds and spectral analysis of the Dirac operator on the associated Poincar\'e-Einstein metric, and relies on combinatorial recurrence identities related to the dual Hahn polynomials.
Keywords
Cite
@article{arxiv.1405.7304,
title = {On Conformal Powers of the Dirac Operator on Einstein Manifolds},
author = {Matthias Fischmann and Christian Krattenthaler and Petr Somberg},
journal= {arXiv preprint arXiv:1405.7304},
year = {2021}
}
Comments
Conformal and semi-Riemannian {\it Spin}-geometry, conformal powers of the Dirac operator, Einstein manifolds, higher variations of the Dirac operator, Hahn polynomials