SavedAdd your journal

Journals / International Electronic Journal of Geometry / 2016 / Cilt: 9 - Sayı: 1

Projective Surfaces and Pre-Normalized Blaschke Immersions of Codimension Two

Atsushi FUJİOKA
Hitoshi FURUHATA
Takeshi SASAKİ
Pages
100–110
Publication Date
2022-10-18
DOI
—
🏛️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 minimalpre-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 minimalpre-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 minimalpre-normalized Blaschke immersion into the equicentroaffine 4-space. Furthermore, an indefinite

🔖

Cite This Article

FUJİOKA, A., FURUHATA, H., SASAKİ, T. (2022). Projective Surfaces and Pre-Normalized Blaschke Immersions of Codimension Two. International Electronic Journal of Geometry, Cilt: 9 - Sayı: 1, 100–110. https://ajindex.com/articles/539705

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (13)

  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
  9. Kobe University, 1999
  10. Sasaki T., Line congruence and transformation of projective surfaces, Kyushu J. Math. 60(2006), no. 1, 101–243
  11. 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
  12. Walter, R., Centroaffine differential geometry: submanifolds of codimension 2, Results Math. 13(1988), no. 3-4, 386-402
  13. Yang Y. and Liu H.-L., Minimal centroaffine immersions of codimension two, Results Math. 52(2008), no. 3-4, 423–437.