Araştırma Makalesi
BibTex RIS Kaynak Göster

EINSTEIN MANIFOLDS AS AFFINE HYPERSURFACES

Yıl 2015, Cilt: 8 Sayı: 1, 33 - 44, 30.04.2015
https://doi.org/10.36890/iejg.592795

Öz



Kaynakça

  • [1] Chen, B.-Y., Ricci curvature of real hypersurfaces in complex hyperbolic space, Arch. Math. (Brno) 38 (2002), 73-80.
  • [2] Chen, B.-Y., A Riemannian invariant and its applications to Einstein manifolds, Bull. Austral. Math. Soc. 70 (2004), 55–65.
  • [3] Chen, B.-Y., An optimal inequality and extremal classes of affine spheres in centroaffine geometry, Geom. Dedicata 111 (2005), 187–210.
  • [4] Chen, B.-Y., Geometry of affine warped product hypersurfaces, Results Math. 48 (2005), 9–26.
  • [5] Chen, B.-Y., Eigenvalue of a natural operator of centro-affine and graph hypersurfaces, Beitr¨age Algebra Geom. 47 (2006), no. 1, 15–27.
  • [6] Chen, B.-Y., Realizations of Robertson-Walker space-times as affine hypersurfaces, J. Phys. A, 40 (2007), 4241–4250.
  • [7] Chen, B.-Y., Pseudo-Riemannian Geometry, δ-invariants and Applications, World Scientific, Hackensack, NJ, 2011.
  • [8] Chen, B.-Y., Total Mean Curvature and Submanifolds of Finite Type. Second Edition, World Scientific, Hackensack, NJ, 2015.
  • [9] Chen, B.-Y., Dillen, F. and Verstraelen, L., δ-invariants and their applications to centroaffine geometry, Differential Geom. Appl. 22 (2005), 341–354.
  • [10] Dillen, F. and Vrancken, L., Calabi-type composition of affine spheres, Differential Geom. Appl. 4 (1994), 303–328.
  • [11] Dillen, F. and Vrancken, L., Improper affine spheres and δ-invariants, PDEs, submanifolds and affine differential geometry, 157–162, Banach Center Publ., 69, Polish Acad. Sci. Inst. Math., Warsaw, 2005.
  • [12] Li, A.-M., Simon, U. and Zhao, G., Global Affine Differential Geometry of Hypersurfaces, Expositions in Mathematics, 11, Walter de Gruyter, Berlin-New York, 1993.
  • [13] Nomizu, K. and Pinkall, U., On the geometry of affine immersions, Math. Z. 195 (1987), 165–178.
  • [14] Nomizu, K. and Sasaki, T., Affine Differential Geometry. Geometry of Affine Immersions, Cambridge Tracts in Math. no. 111 (Cambridge University Press, 1994).
  • [15] Opozda, B., Some relations between Riemannian and affine geometry, Geom. Dedicata 47 (1993), 225–236.
  • [16] Scharlach, C., Simon, U., Verstraelen, L. and Vrancken, L., A new intrinsic curvature invariant for centroaffine hypersurfaces, Beitr¨age Algebra Geom. 38 (1997), no. 2, 437–458.
  • [17] Simon, U., Schwenk-Schellschmidt, A. and Viesel, H., Introduction to the Affine Differential Geometry of Hypersurfaces, Science University of Tokyo, 1991.
  • [18] Vrancken, L., The Magid-Ryan conjecture for equiaffine hyperspheres with constant sectional curvature, J. Differential Geom. 54 (2000), 99–138.
Yıl 2015, Cilt: 8 Sayı: 1, 33 - 44, 30.04.2015
https://doi.org/10.36890/iejg.592795

Öz

Kaynakça

  • [1] Chen, B.-Y., Ricci curvature of real hypersurfaces in complex hyperbolic space, Arch. Math. (Brno) 38 (2002), 73-80.
  • [2] Chen, B.-Y., A Riemannian invariant and its applications to Einstein manifolds, Bull. Austral. Math. Soc. 70 (2004), 55–65.
  • [3] Chen, B.-Y., An optimal inequality and extremal classes of affine spheres in centroaffine geometry, Geom. Dedicata 111 (2005), 187–210.
  • [4] Chen, B.-Y., Geometry of affine warped product hypersurfaces, Results Math. 48 (2005), 9–26.
  • [5] Chen, B.-Y., Eigenvalue of a natural operator of centro-affine and graph hypersurfaces, Beitr¨age Algebra Geom. 47 (2006), no. 1, 15–27.
  • [6] Chen, B.-Y., Realizations of Robertson-Walker space-times as affine hypersurfaces, J. Phys. A, 40 (2007), 4241–4250.
  • [7] Chen, B.-Y., Pseudo-Riemannian Geometry, δ-invariants and Applications, World Scientific, Hackensack, NJ, 2011.
  • [8] Chen, B.-Y., Total Mean Curvature and Submanifolds of Finite Type. Second Edition, World Scientific, Hackensack, NJ, 2015.
  • [9] Chen, B.-Y., Dillen, F. and Verstraelen, L., δ-invariants and their applications to centroaffine geometry, Differential Geom. Appl. 22 (2005), 341–354.
  • [10] Dillen, F. and Vrancken, L., Calabi-type composition of affine spheres, Differential Geom. Appl. 4 (1994), 303–328.
  • [11] Dillen, F. and Vrancken, L., Improper affine spheres and δ-invariants, PDEs, submanifolds and affine differential geometry, 157–162, Banach Center Publ., 69, Polish Acad. Sci. Inst. Math., Warsaw, 2005.
  • [12] Li, A.-M., Simon, U. and Zhao, G., Global Affine Differential Geometry of Hypersurfaces, Expositions in Mathematics, 11, Walter de Gruyter, Berlin-New York, 1993.
  • [13] Nomizu, K. and Pinkall, U., On the geometry of affine immersions, Math. Z. 195 (1987), 165–178.
  • [14] Nomizu, K. and Sasaki, T., Affine Differential Geometry. Geometry of Affine Immersions, Cambridge Tracts in Math. no. 111 (Cambridge University Press, 1994).
  • [15] Opozda, B., Some relations between Riemannian and affine geometry, Geom. Dedicata 47 (1993), 225–236.
  • [16] Scharlach, C., Simon, U., Verstraelen, L. and Vrancken, L., A new intrinsic curvature invariant for centroaffine hypersurfaces, Beitr¨age Algebra Geom. 38 (1997), no. 2, 437–458.
  • [17] Simon, U., Schwenk-Schellschmidt, A. and Viesel, H., Introduction to the Affine Differential Geometry of Hypersurfaces, Science University of Tokyo, 1991.
  • [18] Vrancken, L., The Magid-Ryan conjecture for equiaffine hyperspheres with constant sectional curvature, J. Differential Geom. 54 (2000), 99–138.
Toplam 18 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Bang-yen Chen

Yayımlanma Tarihi 30 Nisan 2015
Yayımlandığı Sayı Yıl 2015 Cilt: 8 Sayı: 1

Kaynak Göster

APA Chen, B.-y. (2015). EINSTEIN MANIFOLDS AS AFFINE HYPERSURFACES. International Electronic Journal of Geometry, 8(1), 33-44. https://doi.org/10.36890/iejg.592795
AMA Chen By. EINSTEIN MANIFOLDS AS AFFINE HYPERSURFACES. Int. Electron. J. Geom. Nisan 2015;8(1):33-44. doi:10.36890/iejg.592795
Chicago Chen, Bang-yen. “EINSTEIN MANIFOLDS AS AFFINE HYPERSURFACES”. International Electronic Journal of Geometry 8, sy. 1 (Nisan 2015): 33-44. https://doi.org/10.36890/iejg.592795.
EndNote Chen B-y (01 Nisan 2015) EINSTEIN MANIFOLDS AS AFFINE HYPERSURFACES. International Electronic Journal of Geometry 8 1 33–44.
IEEE B.-y. Chen, “EINSTEIN MANIFOLDS AS AFFINE HYPERSURFACES”, Int. Electron. J. Geom., c. 8, sy. 1, ss. 33–44, 2015, doi: 10.36890/iejg.592795.
ISNAD Chen, Bang-yen. “EINSTEIN MANIFOLDS AS AFFINE HYPERSURFACES”. International Electronic Journal of Geometry 8/1 (Nisan 2015), 33-44. https://doi.org/10.36890/iejg.592795.
JAMA Chen B-y. EINSTEIN MANIFOLDS AS AFFINE HYPERSURFACES. Int. Electron. J. Geom. 2015;8:33–44.
MLA Chen, Bang-yen. “EINSTEIN MANIFOLDS AS AFFINE HYPERSURFACES”. International Electronic Journal of Geometry, c. 8, sy. 1, 2015, ss. 33-44, doi:10.36890/iejg.592795.
Vancouver Chen B-y. EINSTEIN MANIFOLDS AS AFFINE HYPERSURFACES. Int. Electron. J. Geom. 2015;8(1):33-44.