Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 3 (2007), 084, 14 pages      arXiv:0708.4172
Contribution to the Proceedings of the 2007 Midwest Geometry Conference in honor of Thomas P. Branson

Monogenic Functions in Conformal Geometry

Michael Eastwood a and John Ryan b
a) Department of Mathematics, University of Adelaide, SA 5005, Australia
b) Department of Mathematics, University of Arkansas, Fayetteville, AR 72701, USA

Received August 29, 2007; Published online August 30, 2007

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.

Key words: Clifford analysis; monogenic functions; Dirac operator; conformal invariance.

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