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SIGMA 3 (2007), 084, 14 pages arXiv:0708.4172
https://doi.org/10.3842/SIGMA.2007.084
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
Abstract
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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