Monogenic Functions in Conformal Geometry
Copyright policy )Monogenic Functions in Conformal Geometry
Monogenic functions are basic to Clifford analysis. On Euclidean space they are defined as smooth functions with values in the corresponding Clifford algebra satisfying a certain system of first order differential equations, usually referred to as the Dirac equation. There are two equally natural extensions of these equations to a Riemannian spin manifold only one of which is conformally invariant. We present a straightforward exposition.
This is a contribution to the Proceedings of the 2007 Midwest Geometry Conference in honor of Thomas P. Branson, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
- University of Adelaide Australia
- University of Arkansas United States
- University of Arkansas at Fayetteville United States
- University of Arkansas System United States
- American Mathematical Society United States
monogenic functions, Mathematics - Differential Geometry, conformal invariance, Mathematics - Complex Variables, Dirac operator, Spin and Spin\({}^c\) geometry, Methods of global Riemannian geometry, including PDE methods; curvature restrictions, Clifford algebras, spinors, Invariance and symmetry properties for PDEs on manifolds, Mathematics - Analysis of PDEs, Differential Geometry (math.DG), QA1-939, FOS: Mathematics, Non-Archimedean function theory, Complex Variables (math.CV), Mathematics, Clifford analysis, Analysis of PDEs (math.AP)
monogenic functions, Mathematics - Differential Geometry, conformal invariance, Mathematics - Complex Variables, Dirac operator, Spin and Spin\({}^c\) geometry, Methods of global Riemannian geometry, including PDE methods; curvature restrictions, Clifford algebras, spinors, Invariance and symmetry properties for PDEs on manifolds, Mathematics - Analysis of PDEs, Differential Geometry (math.DG), QA1-939, FOS: Mathematics, Non-Archimedean function theory, Complex Variables (math.CV), Mathematics, Clifford analysis, Analysis of PDEs (math.AP)
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