Journals / International Electronic Journal of Geometry / 2026 / Volume: 9 Issue: 1

Projective Surfaces and Pre-Normalized Blaschke Immersions of Codimension Two

Pages
—
Publication Date
2016-04-30
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Furthermore, an indefinite

📌 3 Key Takeaways

🎯
Objective & Hypothesis:   We prove that any non-degenerate surface in the projective 3-space has a local lift as a minimal pre-normalized Blaschke immersion into the equicentroaffine 4-space.
📊
Key Findings & Data:   We prove that any non-degenerate surface in the projective 3-space has a local lift as a minimal pre-normalized Blaschke immersion into the equicentroaffine 4-space.
💡
Conclusion & Impact:Furthermore, an indefinite
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:projective surface · affine sphere · pre-normalized Blaschke immersion

Abstract

   We prove that any non-degenerate surface in the projective 3-space has a local lift as a minimal pre-normalized Blaschke immersion into the equicentroaffine 4-space. Furthermore, an indefinite

🔖

Cite This Article

Fujioka, A., Furuhata, H., Sasaki, T. (2016). Projective Surfaces and Pre-Normalized Blaschke Immersions of Codimension Two. International Electronic Journal of Geometry, Volume: 9 Issue: 1. https://doi.org/10.36890/iejg.591899

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (12)

  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.