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仿射Khler流形的一类变分问题(英文) 被引量:3

Some variational problems for affine Khler manifold
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摘要 设(M,g)为紧致仿射Khler流形,仿射Kahler度量g=∑fijdxidxj.作者证明了若f满足Δlog(det(fij))=0及Ricci曲率半正定,则M是Rn/Γ,其中Γ为Rn上离散等距子群.进一步,对光滑函数h,作者考虑M上的变分问题,其Euler-Lagrange方程为Δlog(det(fij))=4h(det(fij))-12,通过解这个四阶方程的一类边值问题,构造了定义在Rn上的欧氏完备仿射Kahler流形. Let (M, g) be a n dimenional compact affine Kaehler manifold, its Kaehler metric is g=∑fijdxidxj If Δlog(det(fij)) = 0 and its Ricci curvature Rij≥0, then M must be R^n/Г, where Г be a subgroup of isometric of R^n which acts freely and properly discontinuously on R^n. Moreover, for a smooth function h, a more general volume variational problem on M is considered, the Euler-Lagrange equation is Alog(det(fij ))= 4h (det(f/ij))^-1/2, by solving some boundary problem of the 4-order equation, many Euclidean complete affine Kaehler manifold are constructed.
出处 《四川大学学报(自然科学版)》 CAS CSCD 北大核心 2008年第1期1-9,共9页 Journal of Sichuan University(Natural Science Edition)
基金 国家自然科学基金(10401026)
关键词 仿射Kaehler流形 欧氏完备 affine Kghler manifold, euclidean completeness
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参考文献8

  • 1Cheng S Y, Yau S T. On the real Monge-Ampere equation and affine flat structure[ C]//Chern S S, Wu W T. The 1980 Beijing Symposium Differential Geometry and Differential Equations. Beijing: Science Press, 1982.
  • 2Trudinger N S, Wang X J, The Affine Plateau problem [J].J Amer Math Soc, 2005,18.253.
  • 3Karp L. Subharmonic functions, harmonic mappings and isometric immersions[ C]//Yau S T. Seminar on Differential Geometry. USA: Princeton Univrsity Press, 1982.
  • 4Li A M, Simon U, Zhao G S. Global differential geometry of hypersurfaces[ M]. Berlin/New York:Walter de Gruyter, 1993.
  • 5Calabi E. Hypersurfaces with maximal affinely invariant area[J]. Amer J Math, 1982,104:91.
  • 6Caffarelli L, Nirenbern L, Spruck J. The Dirichlet problem for nonlinear second-order elliptic equations (1), Monge-Amp6re equation [ J ]. Comm Pure Appl Math, 1984,37 : 369.
  • 7Li A M, Simon U, Chen B H, A two-step Monge- Ampeere procedure for solving a fourth order PDE for affine hypersurfaces with constant curvature[J]. J Rein Angew Math, 1997,487 : 179.
  • 8Wang B F, Li A M. The Euclidean complete affine hypersurface with nagetive constant mean curvature. Result in Math, in press.

同被引文献22

  • 1Wang C P. Centroaffine minimal hypersurfaces in R^n+1[J]. Geom Dedicata,1994, 51: 63.
  • 2Li A M, Li H Z, Simon U. Centroaffine Bernstein problems [J]. Diff Geom Appl, 2004, 20: 331.
  • 3Wang B F, Li A M. The Euclidean complete hypersurfaces with negative constant affine mean curvature[J]. Results Math, 2008, 52:383.
  • 4Cheng S Y,Yau S T.On the real Monge-Ampère equation and affine flat structure[C]:Proceedings of the 1980 Beijing Symposium Differential Geometry and Differential Equations,Beijing,China,1980.Beijing:Science Press,1982.
  • 5Shima H,Yagi K.Geometry of Hessian manifold[J].Differential Geometry and Its Applications,1997,73:277.
  • 6Li A M.The affine Khler manifold:report on international congress in Banach Center of Poland[R].Warsaw Poland,2005.
  • 7Li A M,Jia F.A Berstein property of affine maximal hypersurfaces[J].Annals of Global Analysis and Geometry 2003,234:359.
  • 8Jia F,Li A M.Complete Khler affine manifold[J].Submmited.
  • 9Li A M,Jia F.Locally strongly convex hypersurfaces with constant affine mean curvature[J].Differential Geometry and Its Application 2005,222:199.
  • 10Li A M,Jia F.Euclidean complete affine surfaces with affine mean curvature[J].Annals of Global Analysis and Geometry,2003,233:283.

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