Bonnet Ruled Surfaces
Bonnet Ruled Surfaces
摘要
We consider the Bonnet ruled surfaces which admit only one non-trivial isometry that preserves the principal curvatures. We determine the Bonnet ruled surfaces whose generators and orthogonal trajectories form a special net called an A-net.
We consider the Bonnet ruled surfaces which admit only one non-trivial isometry that preserves the principal curvatures. We determine the Bonnet ruled surfaces whose generators and orthogonal trajectories form a special net called an A-net.
参考文献15
-
1Bonnet, O.: Memoire sur la theorie des surfaces applicables sur une surface donee, JF Ecole Pol, Paris(1867), XLII Cahier, 72-92.
-
2Cartan, E.: Sur la couples de surfaces applicables avec conservation des courbures principales. Bull. Soc.Math., 66, 55-85, (1942), or Oeuvres Completes, Ⅲ(2), 1591-1620.
-
3Chern, S. S.: Deformation of surfaces preserving principal curvatures, differential geometry and complex analysis, H E Rauch Memorial Volume, Springer Verlag, 155-163, 1985.
-
4Bobenko, A., I., Eitner, U.: Bonnet surfaces and Painlev6 equations, SFB 288 Preprint 151, TU Berlin,1994.
-
5Bobenko, A. I., Either, V.: Painleve equations in differential geometry of surfaces, SFB 288 Preprint No 449, Berlin, 3-2000.
-
6Roussos, I. M.: Global results on Bonnet surfaces. J. of Geometry, 65, 151-168 (1999).
-
7Soyucok, Z.: The problem of non-trivial isometries of surfaces preserving principal curvatures. Journal of Geometry, 52, 173-188 (1995), Basel.
-
8Roussos,Vi. M.: Tangential developable surfaces as Bonnet surfaces. Acta Mathematica Sinica, English Series, 15(2), 269-276 (1999).
-
9Voss, K.: Bonnet surfaces in spaces of constant curvature, Japan: Lecture Notes Ⅱ of 1^st MSJ Research Institue, Sendai, 295- 307, 1993.
-
10Chen, X., Peng, C. K.: Deformation of surfaces preserving principal curvatures, Lecture Notes in Math.1369, Springer Verlag (Differential Geometry and Topology Proceedings, Tianjin, 1986-1987), 63-70.
-
1Ji-Yao Chen,Zhengfeng Ji,Zheng-Xin Liu,Xiaofei Qi,Nengkun Yu,Bei Zeng,Duanlu Zhou.Physical origins of ruled surfaces on the reduced density matrices geometry[J].Science China(Physics,Mechanics & Astronomy),2017,60(2):1-8.
-
2■RENM■■ Alper Osman,BALGET■R Handan,ERGüT Mahmut.On the Ruled surfaces in Minkowski 3-space R1^3[J].Journal of Zhejiang University-Science A(Applied Physics & Engineering),2006,7(3):326-329.
-
3Jian-fei XIONG School of Mathematical Sciences, Qingdao University, Qingdao 266071, China.The local classifications of the ruled surfaces of normals and binormals of a regular space curve[J].Science China Mathematics,2007,50(4):533-548.
-
4王锋.波动与稳定 三差来裁定[J].初中生学习指导(八年级提升版),2015,0(10):53-55.
-
5周青春,陈铮,董师润.电场辅助阳极连接碱金属耗尽层模型[J].中国有色金属学报,2002,12(6):1268-1271. 被引量:1
-
6周青春,陈铮,董师润.阳极连接模型[J].华东船舶工业学院学报,2002,16(1):82-85.
-
7周青春,陈铮,董师润.点阴极电场辅助阳极连接中的紧密接触面积和电流[J].电子器件,2002,25(1):37-40.
-
8Pingqi Pan.A FAST SIMPLEX ALGORITHM FOR LINEAR PROGRAMMING[J].Journal of Computational Mathematics,2010,28(6):837-847. 被引量:3
-
9张宇鑫,黄达海,刘海成.Solution precision of concrete temperature fields with finite difference method[J].Journal of Shanghai University(English Edition),2008,12(4):302-305. 被引量:2
-
10CHEN Jiaqing,JIN Qianyu,CHEN Zhiqiang,LIU Cihua.Two-Sided Empirical Bayes Test for the Exponential Family with Contaminated Data[J].Wuhan University Journal of Natural Sciences,2013,18(6):466-470.