Abstract
In this paper we characterize affine translation surfaces with constant Gaussian curvature. We show that such surfaces must be flat and that one of the defining curves must be planar.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Burstin, C. and Mayer, W., Die Geometrie zweifach ausgedehnter Mannigfaltigkeiten F2 im affinen Raum R4, Math. Z.27 (1927), 373–407.
Klingenberg, W.Zur affinen Differentialgeometrie, Teil II: Uber 2-dimensionale Flächen im 4-dimensionalen Raum, Math. Z.54 (1951), 184–216.
Nomizu, Katsumi and Sasaki, Takeshi,Affine Differential Geometry, Cambridge, Cambridge, 1994.
Nomizu, K. and Vrancken, L.,A new equiaffine theory for surfaces in R4, International J. Math.4 (1993), 127–165.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Magid, M., Vrancken, L. Affine translation surfaces with constant sectional curvature. J Geom 68, 192–199 (2000). https://doi.org/10.1007/BF01221071
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01221071