Projective Surfaces and Pre-Normalized Blaschke Immersions of Codimension Two
We prove that any non-degenerate surface in the projective 3-space has a local lift as a minimalpre-normalized Blaschke immersion into the equicentroaffine 4-space. Furthermore, an indefinite
___
- [1] Ferapontov, E. V., Integrable systems in projective differential geometry, Kyushu J. Math.
54(2000), no. 1, 183–215.
- [2] Fujioka A., Furuhata H. and Sasaki T., Projective minimality for centroaffine minimal
surfaces, J. Geom. 105(2014), no. 1, 87–102.
- [3] Furuhata H., Minimal centroaffine immersions of
codimension two, Bull. Belg. Math. Soc. 7(2000), no. 1, 125–134.
- [4] Liu H.-L., Indefinite equi-centroaffinely homogeneous surfaces with vanishing Pick-invariant
in R4, Math. J. 26(1997), no. 1, 225–251.
- [5] Lopšic, A. M., On the theory of a surface of n dimensions in an equicentroaffine space of n +
2 dimensions, (Russian) Sem. Vektor. Tenzor. Analizu. 8(1950), 286–295.
- [6] Nomizu K. and Sasaki T., Centroaffine immersions of codimension two and projective
hypersurface theory, Nagoya Math. J. 132(1993), 63–90.
- [7] Nomizu K. and Sasaki T., Affine differential geometry. Geometry of affine immersions,
Cambridge Tracts in Mathematics, 111, Cambridge University Press, Cambridge, 1994.
- [8] Sasaki T., Projective differential geometry and linear homogeneous differential equations,
Rokko Lectures in Math. 5. Kobe University, 1999.
- [9] Sasaki T., Line congruence and transformation of projective surfaces, Kyushu J. Math. 60(2006), no. 1, 101–243.
- [10] Simon, U., Schwenk-Schellschmidt, A. and Viesel, H., Introduction to the affine differential
geometry of hypersurfaces, Lecture Notes of the Science University of Tokyo, Science University of
Tokyo, Tokyo, 1991.
- [11] Walter, R., Centroaffine differential geometry: submanifolds of codimension 2, Results Math.
13(1988), no. 3-4, 386-402.
- [12] Yang Y. and Liu H.-L., Minimal centroaffine immersions of codimension two, Results Math.
52(2008), no. 3-4, 423–437.