Centroaffine Minimal Surfaces with Constant Curvature Metric

  • 투고 : 2004.12.01
  • 발행 : 2006.06.23

초록

We classify centroaffine minimal surfaces with constant curvature metric under some natural conditions on the cubic differentials.

키워드

참고문헌

  1. T. Binder, Local classification of centroaffine Tchebychev surfaces with constant curvature metric, Geometry and topology of submanifolds, IX (Valenciennes/ Lyon/Leuven, 1997), 27-32, World Sci. Publishing, River Edge, NJ, 1999.
  2. W. Blaschke, Vorlesungen uber Differentialgeometrie II, Affine Differentialgeometrie, Springer, Berlin, 1923.
  3. A. I. Bobenko, Surfaces in terms of 2 by 2 matrices. Old and new integrable cases, Harmonic maps and integrable systems, 83-127, Aspects Math., E23, Vieweg, Braunschweig, 1994.
  4. A. G. Colares and K. Kenmotsu, Isometric deformation of surfaces in preserving the mean curvature function, Pacific J. Math., 136(1)(1989), 71-80. https://doi.org/10.2140/pjm.1989.136.71
  5. A. Fujioka, Bianchi surfaces with constant Chebyshev angle, Tokyo J. Math., 27(1)(2004), 149-153. https://doi.org/10.3836/tjm/1244208481
  6. H. L. Liu and C. P.Wang, The centroaffine Tchebychev operator, Festschrift dedicated to Katsumi Nomizu on his 70th birthday (Leuven, 1994; Brussels, 1994). Results Math., 27(1-2)(1995), 77-92. https://doi.org/10.1007/BF03322271
  7. M. A. Magid and P. J. Ryan, Flat affine spheres in $R^3$, Geom. Dedicata, 33(3)(1990), 277-288.
  8. W. K. Schief, Hyperbolic surfaces in centro-affine geometry. Integrability and discretization, Integrability and chaos in discrete systems (Brussels, 1997). Chaos Solitons Fractals 11(1-3)(2000), 97-106. https://doi.org/10.1016/S0960-0779(98)00273-2
  9. U. Simon, Local classification of two-dimensional affine spheres with constant curvature metric, Differential Geom. Appl., 1(2)(1991), 123-132. https://doi.org/10.1016/0926-2245(91)90026-6
  10. G. Tzitzeica, Sur une nouvelle classe de surfaces, C. R. Acad. Sci. Paris, 144(1907), 1257-1259; 146(1908), 165-166.
  11. G. Tzitzeica, Sur une nouvelle classe de surfaces, C. R. Acad. Sci. Paris, 146(1908), 165-166.
  12. G. Tzitzeica, Sur une nouvelle classe de surfaces, Rendi. Circ. Mat. Palermo, 25 (1908), 180-187 https://doi.org/10.1007/BF03029121
  13. G. Tzitzeica, Sur une nouvelle classe de surfaces, Rendi. Circ. Mat. Palermo, 28 (1909), 210-216. https://doi.org/10.1007/BF03018218
  14. G. Tzitzeica, Sur une nouvelle classe de surfaces, C. R. Acad. Sci. Paris, 150(1910), 955-956, 1227-1229.
  15. C. P. Wang, Centroaffine minimal hypersurfaces in $R^{n+1}$, Geom. Dedicata, 51(1)(1994), 63-74. https://doi.org/10.1007/BF01264101