Abstract
In this paper we study affine nondegenerate Blaschke immersions from a surface M in ℝ3 which induce locally symmetric Blaschke structures on M. We shall give in local coordinates detailed description of such immersions and induced Blaschke structures.
Similar content being viewed by others
References
Dillen, F., ‘Locally symmetric complex affine hypersurfaces’, J. Geometry 33 (1988), 27–38.
Dillen, F., ‘Equivalence theorems in affine differential geometry’, Geom. Dedicata 32, 81–92 (1989).
Jelonek, W., ‘Affine surfaces with parallel shape operators’ Annales Polon. Math. LV1.2, 179–186 (1992).
Kobayashi, S. and Nomizu, K., Foundations of Differential Geometry, Vol. 1, Interscience Publishers, New York, London, Sydney, 1969.
Lamb, G. L. Jr, ‘Elements of Soliton Theory, Interscience, New York, Chichester, Brisbane, Toronto, 1980.
Miller, W. Jr, Symmetry and Separation of Variables, Addison-Wesley, 1977.
Nomizu, K., ‘On completeness in affine differential geometry’, Geom. Dedicata 20 (1986), 43–49.
Nomizu, K. and Pinkall, U., ‘On the geometry of affine immersions’, Math. Z. 195 (1987), 165–178.
Simon, U., Proc. of Conf. on Differential Geometry and its Applications, Proc. Yugoslavia, 1988.
Slebodzinski, W., ‘Sur une classe de l'espace affine’, C.R. Acad. Sci.Paris, 1937.
Verheyen, P., and Verstraelen, L., ‘Locally symmetric hypersurfaces in an affine space’, Proc. Amer. Math. Soc. 93, (1985), 101–105.
Vrancken, L., ‘Affine surfaces with constant affine curvatures’, Geom. Dedicata 33 (1990) 177–194.
Yau, Chi-Ming, ‘Affine conormal of convex hypersurfaces’, Proc. Amer. Math. Soc. 106 (1989), 2, 465–470.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Jelonek, W. Affine locally symmetric surfaces. Geom Dedicata 44, 189–221 (1992). https://doi.org/10.1007/BF00182949
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00182949