Article ID Journal Published Year Pages File Type
4606635 Differential Geometry and its Applications 2009 10 Pages PDF
Abstract

The algebra of differential invariants of a suitably generic surface S⊂R3S⊂R3, under either the usual Euclidean or equi-affine group actions, is shown to be generated, through invariant differentiation, by a single differential invariant. For Euclidean surfaces, the generating invariant is the mean curvature, and, as a consequence, the Gauss curvature can be expressed as an explicit rational function of the invariant derivatives, with respect to the Frenet frame, of the mean curvature. For equi-affine surfaces, the generating invariant is the third order Pick invariant. The proofs are based on the new, equivariant approach to the method of moving frames.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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