Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2016, Cilt: 9 Sayı: 1, 100 - 110, 30.04.2016
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
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.

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 Bu kişi benim

Hitoshi Furuhata Bu kişi benim

Takeshi Sasaki Bu kişi benim

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.