Affine surfaces with constant affine curvatures

✍ Scribed by Luc Vrancken

• Publisher: Springer
• Year: 1990
• Tongue: English
• Weight: 552 KB
• Volume: 33
• Category: Article
• ISSN: 0046-5755
• DOI: 10.1007/bf00183083

✦ Synopsis

AFFINE SURFACES WITH CONSTANT AFFINE CURVATURES

AIkSTRACT. In this paper, we study atfine non-degenerate Blaschke immersions from a surface M in R 3. We will assume that M has constant affine curvature and constant affine mean curvature, i.e. both the determinant and the trace of the shape operator are constant. Clearly, affine spheres satisfy both these conditions. In this paper, we completely classify the afline surfaces with constant attine curvature and constant affine mean curvature, which are not affine spheres.