Journal of Differential Geometry

Convex decompositions of real projective surfaces. II. Admissible decompositions

Suhyoung Choi

Full-text: Open access

Article information

Source
J. Differential Geom., Volume 40, Number 2 (1994), 239-283.

Dates
First available in Project Euclid: 26 June 2008

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1214455537

Digital Object Identifier
doi:10.4310/jdg/1214455537

Mathematical Reviews number (MathSciNet)
MR1293655

Zentralblatt MATH identifier
0822.53009

Subjects
Primary: 57M50: Geometric structures on low-dimensional manifolds

Citation

Choi, Suhyoung. Convex decompositions of real projective surfaces. II. Admissible decompositions. J. Differential Geom. 40 (1994), no. 2, 239--283. doi:10.4310/jdg/1214455537. https://projecteuclid.org/euclid.jdg/1214455537


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References

  • [1] J. Benzecri, Sur les varietes localement affine set projective, Bull. Soc.Math. France 88 (1960) 229-332.
  • [2] Y. Carriere, Autour de la conjecture de L. Markus sur les varietes affines, Invent. Math. 95 (1989) 615-628.
  • [3] A. Casson and S. Bleiler, Automorphisms of surfaces after Nielsen and Thurston, London Math. Soc.Student Texts, Vol. 9, Cambridge Univ. Press, Cambridge, 1988.
  • [4] S. Choi, Real projective surfaces, Ph.D.thesis, Princeton Univ., 1988.
  • [5] S. Choi, Real projective surfaces, Convex decompositions of real projective surfaces. I: -Annuli and convexity, to appear.
  • [6] S. Choi, Real projective surfaces, Convex decompositions of realprojective surfaces. Ill, to appear.
  • [7] S. Choi, Real projective surfaces, Convex decompositions of realprojective surfaces. IV, to appear.
  • [8] S. Choi and W. Goldman, Deformationspaces of real projective structures on compact surfaces, to appear.
  • [9] G. Faltings, Real projective structures on Riemann surfaces, Compositio Math. 48 (1983) 223-269.
  • [10] M.Freedman, J. Hass and P. Scott, Closed geodesics on surfaces, Bull. London Math. Soc. 14 (1982) 385-391.
  • [11] D. Fried, Closed similarity manifolds, Comment. Math. Helv. 55 (1980) 709-719.
  • [12] D.Gallo, W. Goldman and R. Porter, Projective structures with monodromyin PSL(2, R), preprint.
  • [13] W. Goldman, Affine manifolds with projective geometry on surfaces, Senior thesis, Princeton Univ., 1977.
  • [14] W. Goldman, Projective structures with Fuchsian holonomy, J. Differential Geometry 25 (1987) 297-326.
  • [15] W. Goldman, Projective geometry on manifolds, Lecture notes, Univ. Maryland.
  • [16] W. Goldman, Convex real projective structures on compact surfaces, J. Differential Geometry 31 (1990) 791-845.
  • [17] V. Kac and E. B. Vinberg, Quasi-homogeneous cones, Mat. Zametki 1 (1967) 347-354, English transl., Math. Notes 1 (1967), 231-235.
  • [18] Y. Kamishima and S. Tan, Deformation spaces on geometric structures, Aspects of Low Dimensional Manifolds, (Y. Matsumoto & S. Morita, eds.), Advanced Studies in Pure Math., Vol. 20, Kinokuniya, Tokyo, 1922.
  • [19] J. L. Koszul, Varietes localement plates et convexite, Osaka J. Math. 2 (1965) 285-290.
  • [20] N. Kuiper, On convex locally projective spaces, Convegno Intenazionale di Geometria Differenziale, Rome, 1953, 200-213.
  • [21] B. Maskit, Kleinian groups, Grundlehren Math. Wiss., Vol. 287, Springer, Berlin, 1988.
  • [22] J. Milnor, On the existence of a connection with curvature zero, Comment. Math. Helv. 32 (1958) 215-223.
  • [23] P. Scott, Subgroups of surface groups are almost geometric, J. London Math. Soc. (2) 17 (1978) 555-565.
  • [24] P. Scott, Correction to ''Subgroups ofsurface groups are almostgeometric"', J. London Math. Soc. (2) 32 (1985) 217-220.
  • [25] J. Simillie, Affinelyflat manifolds, Ph.D. thesis, Univ. Chicago, 1977.
  • [26] D. Sullivan and W. Thurston, Manifolds with canonical coordinate charts: Some examples, Enseignement Math. 29 (1983) 15-25.
  • [27] W. Thurston, The geometry and topology of three-manifolds, preprint.

See also

  • Part I: Suhyoung Choi. Convex decompositions of real projective surfaces. I. $\pi$-annuli and convexity. J. Differential Geom., Volume 40, Number 1, (1994), 165--208.