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R3,1中类时曲面的广义Weierstrass表示 被引量：2

Generalized Weierstrass Representation of Timelike Surface in R3,1
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摘要 证明了四维Minkowski空间R3,1中的正则类时曲面，局部上都由广义Weierstrass公式确定。 In this paper, the authors prove that every regular timelike surface with null coordinates system in 4-dimensional Minkowski space R3,1 is locally determined by generalized Weierstrass formulae.
作者 陈建华 林敏
机构地区 装甲兵工程学院基础部
出处 《装甲兵工程学院学报》 2009年第3期84-86,共3页 Journal of Academy of Armored Force Engineering
基金 国家自然科学基金资助项目(10561010)
关键词 共形浸入 WEIERSTRASS表示 MINKOWSKI空间 conformal immersion Weierstrass representation Minkowski space
分类号 O186 [理学—基础数学]
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参考文献5

  • 1Bryant R.Surface of Mean Curvature One in Hyperbolic Space[J].Asterisque,1987(154-155):321 -347.
  • 2Hu H.Sine-Laplace Equations,Sinh-Laplace Equations and Harmonic Maps[J].Manuscripta Math,1982(40):205 -216.
  • 3Umehara M,Yamada K.A Parametrization of Weierstrass Formulae and Perturbation of Complete Minimal Surface in R3 into the Hyperbolic Space[J].J Relne Angew Math,1992(432):93 -116.
  • 4Konopelchenko B G.Weierstrass Representations for Surfaces in 4D Spaces and Their lntegrable Deformations via DS Hierarchy[J].Annals of Global Analysis and Geometry,2000(18):61 -74.
  • 5Chen J H,Chen W H.The Generalized Weierstrass Representation of Surfaces in R4[J].J Geom and Phya,2007(57):367 -378.

同被引文献17

  • 1Bryant R. Surface of Mean Curvature One in Hyperbolic Space[J]. Asterisque,1987(154/155) : 321 -347.
  • 2Dorfmeister J, Inoguchi J, Toda M. Weierstrass Type Represen- tation of Timelike Surface with Constant Mean Curvature, Diff Geom and Integrable System [ J ]. Contemporary Mathematics AMS, 2002 (308) :1 -41.
  • 3Konopelchenko B G, Taimanov I A. Constant Mean Curvature Surfaces via an Integrable Dynamical System [J].J Phys A:Math Gen, 1996 (29) :1261 - 1265.
  • 4Chen J H, Chen W H. The Generalized Weierstrass Representation of Surfaces in R^4 [ J ]. J Geom and Phys, 2007 (57) : 367 - 378.
  • 5Konopelchenko B G. Induced Surfaces and their Integrable Dy- namics[J]. Stud Appl Math, 1996(96) :9 -51.
  • 6Qing c, Yi c. Spectral Translormation ot Constant Mean Curva- ture Surfaces in 1/3 and Weierstrass Representation [ J ]. Science in China: A, 2002 (8) : 1066 -1075.
  • 7Pedit F, Pinkall U. Quaternionic Analysis on Riemann Surfaces and Differential Geometry [ J ]. Document Mathematic, Extra Volume ICM, 1998 (II) : 389 - 400.
  • 8Umehara M, Yamada K. A Parameterization of Weierstrass For- mulae and Perturbation of Complete Minimal Surface in R3 into the Hyperbolic Space[J]. J Reine Angew Math, 1992(432) :93 -116.
  • 9Chen J H, Guo Z, Lin M. The Spacelike Surface With Parallel Mean Curvature Vector in R^3'1 [ J ]. Journal of Geometry and Physics, 2009 (59) : 340 - 353.
  • 10Bobenko A I. All Constant Mean Curvature Torl in R3 ; S3 ; H3 in Terms of Theta-functions[ J]. Math Ann, 1991, 290( 1 ) : 209 - 245.

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装甲兵工程学院学报
2009年 第3期

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