Araştırma Makalesi
BibTex RIS Kaynak Göster

Yıl 2016, Cilt: 9 Sayı: 1, 100 - 110, 30.04.2016

Atsushi Fujioka Hitoshi Furuhata Takeshi Sasaki

https://doi.org/10.36890/iejg.591899

Öz

Kaynakça

  • [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.

Projective Surfaces and Pre-Normalized Blaschke Immersions of Codimension Two

Yıl 2016, Cilt: 9 Sayı: 1, 100 - 110, 30.04.2016

Atsushi Fujioka Hitoshi Furuhata Takeshi Sasaki

https://doi.org/10.36890/iejg.591899

Öz

   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
surface in the projective 3-space has a local lift as a pre-normalized Blaschke immersion into the
equicentroaffine 4-space satisfying the Einstein condition if and only if the surface is projectively
applicable to an affine sphere.

Anahtar Kelimeler

projective surface affine sphere pre-normalized Blaschke immersion centroaffine minimality Einstein condition

Kaynakça

  • [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.
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Atsushi Fujioka

Hitoshi Furuhata

Takeshi Sasaki

Yayımlanma Tarihi 30 Nisan 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 9 Sayı: 1

Kaynak Göster

APA Fujioka, A., Furuhata, H., & Sasaki, T. (2016). Projective Surfaces and Pre-Normalized Blaschke Immersions of Codimension Two. International Electronic Journal of Geometry, 9(1), 100-110. https://doi.org/10.36890/iejg.591899
AMA Fujioka A, Furuhata H, Sasaki T. Projective Surfaces and Pre-Normalized Blaschke Immersions of Codimension Two. Int. Electron. J. Geom. Nisan 2016;9(1):100-110. doi:10.36890/iejg.591899
Chicago Fujioka, Atsushi, Hitoshi Furuhata, ve Takeshi Sasaki. “Projective Surfaces and Pre-Normalized Blaschke Immersions of Codimension Two”. International Electronic Journal of Geometry 9, sy. 1 (Nisan 2016): 100-110. https://doi.org/10.36890/iejg.591899.
EndNote Fujioka A, Furuhata H, Sasaki T (01 Nisan 2016) Projective Surfaces and Pre-Normalized Blaschke Immersions of Codimension Two. International Electronic Journal of Geometry 9 1 100–110.
IEEE A. Fujioka, H. Furuhata, ve T. Sasaki, “Projective Surfaces and Pre-Normalized Blaschke Immersions of Codimension Two”, Int. Electron. J. Geom., c. 9, sy. 1, ss. 100–110, 2016, doi: 10.36890/iejg.591899.
ISNAD Fujioka, Atsushi vd. “Projective Surfaces and Pre-Normalized Blaschke Immersions of Codimension Two”. International Electronic Journal of Geometry 9/1 (Nisan 2016), 100-110. https://doi.org/10.36890/iejg.591899.
JAMA Fujioka A, Furuhata H, Sasaki T. Projective Surfaces and Pre-Normalized Blaschke Immersions of Codimension Two. Int. Electron. J. Geom. 2016;9:100–110.
MLA Fujioka, Atsushi vd. “Projective Surfaces and Pre-Normalized Blaschke Immersions of Codimension Two”. International Electronic Journal of Geometry, c. 9, sy. 1, 2016, ss. 100-1, doi:10.36890/iejg.591899.
Vancouver Fujioka A, Furuhata H, Sasaki T. Projective Surfaces and Pre-Normalized Blaschke Immersions of Codimension Two. Int. Electron. J. Geom. 2016;9(1):100-1.