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

SIGMA 3 (2007), 097, 15 pages      arXiv:0710.0519      https://doi.org/10.3842/SIGMA.2007.097
Contribution to the Proceedings of the 2007 Midwest Geometry Conference in honor of Thomas P. Branson

Differential Invariants of Conformal and Projective Surfaces

Evelyne Hubert a and Peter J. Olver b
a) INRIA, 06902 Sophia Antipolis, France
b) School of Mathematics, University of Minnesota, Minneapolis 55455, USA

Received August 15, 2007, in final form September 24, 2007; Published online October 02, 2007

Abstract
We show that, for both the conformal and projective groups, all the differential invariants of a generic surface in three-dimensional space can be written as combinations of the invariant derivatives of a single differential invariant. The proof is based on the equivariant method of moving frames.

Key words: conformal differential geometry; projective differential geometry; differential invariants; moving frame; syzygy; differential algebra.

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