Parallel surfaces in affine 4-space

Details Parallel surfaces in affine 4-space Parallel surfaces in affine 4-space

2002-10-25

arxiv.org/abs/math/0210406v1

Mathematics

Differential Geometry

16 pages, 1 figure (uses epsf.tex), submitted for publication

Scientific paper

We study affine immersions as introduced by Nomizu and Pinkall. We classify
those affine immersions of a surface in 4-space which are degenerate and have
vanishing cubic form (i.e. parallel second fundamental form). This completes
the classification of parallel surfaces of which the first results were
obtained in the beginning of this century by Blaschke and his collaborators.

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