Parallel surfaces in affine 4-space

2002/10/25 by C. Scharlach, Christine Scharlach, Scharlach, C. +3
Computer Science · Engineering · Mathematics · #53A15 #Advanced Numerical Analysis Techniques #Computational Geometry and Mesh Generation #Differential Geometry (math.DG) #FOS: Mathematics #Mathematics and Applications #math.DG #msc:53A15

paper · pdf · doi:10.48550/arxiv.math/0210406

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

arxiv created 2002/10/25 · openalex publication_date 2002/10/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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