Author: F. Manhart 1
View More View Less
  • 1 Institute für Geometrie, Technische Universität Wiedner Hauptstrasse 8-10, A-1040 Wien, Austria
Restricted access

Purchase article

USD  $25.00

1 year subscription (Individual Only)

USD  $800.00

We give a classification of affine rotation surfaces in affine 3-space with flat affine metric.

  • Blaschke, W., Vorlesungen über Differentialgeometrie, Band II: Affine Differentialgeometrie, Springer (Berlin, 1923).

    Vorlesungen über Differentialgeometrie, Band II: Affine Differentialgeometrie , ().

    • Search Google Scholar
  • Lehebel, P., Affine rotation surfaces and hypersurfaces, in: Geometry and Topology of Submanifolds (F. Dillen et al., editors), VIII. Proceedings on meetings in Belgium (13-14 July 1995) and Norway (18 July-7 August 1995), World Scientific Publishing Co.Pte.Ltd. (1996), pp. 198-208. MR 98a:53015

    Geometry and Topology of Submanifolds , () 198 -208.

  • Magid, M. and Ryan, P., Flat affine spheres in R3, Geometriae Dedicata 33 (1990), 277-288. MR 91e:53016

    'Flat affine spheres in R3 ' () 33 Geometriae Dedicata : 277 -288.

  • Manhart, F., Affine surfaces of rotation with vanishing affine curvature, J. Geom. (submitted).

  • SÜSS, W., Ein affingeometrisches Gegenstück zu den Rotationsflächen, Math. Ann. 98 (1928), 684-696.

    'Ein affingeometrisches Gegenstück zu den Rotationsflächen ' () 98 Math. Ann. : 684 -696.

    • Search Google Scholar
  • Schirokow, P.U.A., Affine Differentialgeometrie. B. G. Teubner (Leipzig, 1962).

    Affine Differentialgeometrie. , ().

  • Su, B., Affine moulding surfaces and affine surfaces of revolution, Tohoku Math. J. 5 (1928), 185-210. MR 27#660

    'Affine moulding surfaces and affine surfaces of revolution ' () 5 Tohoku Math. J. : 185 -210.

    • Search Google Scholar
  • Dillen, F. Et Al., On the Pick invariant, the affine mean curvature and the Gauss curvature of affine surfaces, Res. Math. 20 (1991), 622-642. MR 93h:53015

    'On the Pick invariant, the affine mean curvature and the Gauss curvature of affine surfaces ' () 20 Res. Math. : 622 -642.

    • Search Google Scholar
  • Krauter, P., Affine minimal hypersurfaces of rotation, Geometriae Dedicata 51 (1994), 287-303. MR 95f:53019

    'Affine minimal hypersurfaces of rotation ' () 51 Geometriae Dedicata : 287 -303.

  • Lee, I. C., On generalized affine rotation surfaces, Res. Math. 27 Nr. 1-2 (1995), 63-76. MR 95m:53011

    'On generalized affine rotation surfaces ' () 27 Res. Math. : 1 -2.

  • Lee, I. C., Projectively flat affine surfaces that are not locally symmetric, Proceedings of the AMS. 123 Nr. 1 (1995), 237-246. MR 95c:53011

    'Projectively flat affine surfaces that are not locally symmetric ' () 123 Proceedings of the AMS. : 237 -246.

    • Search Google Scholar
  • Lee, I. C. and Vrancken, L., Projectively flat affine surfaces with flat affine metric, J. Geom. 70 (2001), 85-100. MR 2001m:53020

    'Projectively flat affine surfaces with flat affine metric ' () 70 J. Geom. : 85 -100.