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EINSTEIN MANIFOLDS AS AFFINE HYPERSURFACES

Year 2015, Volume: 8 Issue: 1, 33 - 44, 30.04.2015
https://doi.org/10.36890/iejg.592795

Abstract



References

  • [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.
Year 2015, Volume: 8 Issue: 1, 33 - 44, 30.04.2015
https://doi.org/10.36890/iejg.592795

Abstract

References

  • [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.
There are 18 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Bang-yen Chen

Publication Date April 30, 2015
Published in Issue Year 2015 Volume: 8 Issue: 1

Cite

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. April 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, no. 1 (April 2015): 33-44. https://doi.org/10.36890/iejg.592795.
EndNote Chen B-y (April 1, 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., vol. 8, no. 1, pp. 33–44, 2015, doi: 10.36890/iejg.592795.
ISNAD Chen, Bang-yen. “EINSTEIN MANIFOLDS AS AFFINE HYPERSURFACES”. International Electronic Journal of Geometry 8/1 (April 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, vol. 8, no. 1, 2015, pp. 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.