[1] Calabi E. Complete affine hyperspheres I//Symposia Mathematica. London: Academic Press (10), 1972: 19-38
[2] Cao F, Tian C. Integrable system and spacelike surfaces with proscribed weak curvature in Minkowski 3-space. Acta Math Sci, 1999, 19(1): 91-96
[3] Cheng S Y, Yau S T. On the existence of a complete Kähler metric on noncompact complex manifolds and the regularity of Fefferman's equation. Comm Pure Appl Math, 1980, 33(4): 507-544
[4] Cheng S Y, Yau S T. The real Monge-Ampère equation and affine flat structures//Proc 1980 Beijing Symp on Diff Geom and Diff Equ, vol 1. Beijing: Science Press, 1982: 339-370
[5] Cheng S Y, Yau S T. Complete affine hyperspheres part I, The completeness of affine metrics. Comm Pure Appl Math, 1986, 39(6): 839-866
[6] Chern S S. An elementary proof of the existence of isothermal parameters on a surface. Proc Amer Math Soc, 1955, 6(5): 771-782
[7] Dorfmeister J, Eitner U. Weierstrass-type representation of affine sphere. Abh Math Sem Univ Hamburg, 2001, 71: 225-250
[8] Dorfmeister J, Wang E X. Definite affine spheres via loop groups Ⅰ: general theory. (preprint)
[9] Dorfmeister J, Wang E X. Definite affine spheres via loop groups Ⅱ: equivariant solutions. (draft)
[10] Dunajski M, Plansangkate P. Strominger-Yau-Zaslow geometry, affine spheres and Painlevé Ⅲ. Commun Math Phys, 2009, 290: 997-1024
[11] Fox D J F. A Schwarz lemma for Kähler affine metrics and the canonical potential of a proper convex cone. arXiv e-print math. DG: 1206.3176, 2012
[12] Guest M. Harmonic Maps, Loop Groups, and Integrable Systems. Cambridge University Press, 1997
[13] Hancock H. Theory of Elliptic Functions. New York: Dover, 1958
[14] Hildebrand R. Einstein-Hessian barriers on convex cones. Optimization Online e-print 2012/05/3474, 2012
[15] Hildebrand R. Analytic formulas for complete hyperbolic affine spheres. Beitrage zur Algebra und Geometrie/Contributions to Algebra and Geometry, 2014, 55(2): 497-520
[16] Kaptsov O V, Shan'ko Yu V. Trilinear representation and the Moutard transformation for the Tzitzeica equation. arXiv: solv-int/9704014v1
[17] Lang S. Elliptic Functions. New York: Springer, 1987
[18] Li A M, Simon U, Zhao G S. Global Affine Differential Geometry of Hypersurfaces. Volume 11 of De Gruyter Expositions in Mathematics. Walter de Gruyter, 1993
[19] Li W, Han Y, Zhou G. Damboux transformation of a nonlinear evolution equation and its explicit solutions. Acta Math Sci, 2011, 31(4): 1457-1464
[20] Lin Z C, Wang G, Wang E X. Dressing actions on proper definite affine spheres. arXiv:1502.04766
[21] Loftin J C. Affine spheres and Kähler-Einstein metrics. Math Res Lett, 2002, 9(4): 425-432
[22] Loftin J, Yau S T, Zaslow E. Affine manifolds, SYZ geometry and the Y vertex. J Differ Geom, 2005, 71(1): 129-158
[23] Simon U, Wang C P. Local theory of affine 2-spheres. Proc Symposia Pure Math, 1993, 54: 585-598
[24] Spivak M. A Comprehensive Introduction to Differential Geometry 4. 3rd ed. Publish or Perish Inc, tome, 1999: 314-346
[25] Terng C L. Geometries and symmetries of soliton equations and integrable elliptic equations. Surveys Geometry Integrable Systems, 2008, 30: 401-488
[26] Tian C, Zhou K H, Tian C B. Blacklund transformation on surfaces with constant mean curvature in R2. Acta Math Sci, 2003, 23(3): 369-376
[27] Uhlenbeck K. Harmonic maps into Lie groups (classical solutions of the chiral model). J Diff Geom, 1989, 30: 1-50
[28] Wang E X. Tzitzéica transformation is a dressing action. J Math Phys, 2006, 47(5): 875-901
[29] Wang G, Lin Z C, Wang E X. Permutability theorem for definite affine spheres and the group structure of dressing actions. (preprint)
[30] Zakharov V E, Shabat A B. Integration of non-linear equations of mathematical physics by the inverse scattering method II. Funct Anal Appl, 1979, 13: 166-174 |