三维Minkowski空间中的一类螺旋面
A Kind of Helicoidal Surface in 3-Dimensional Minkowski Space
DOI: 10.12677/PM.2015.54021, PDF, HTML, XML, 下载: 2,324  浏览: 6,301  科研立项经费支持
作者: 吴 珩, 黄平亮：上海大学理学院数学系，上海
关键词: Minkowski空间；螺旋面；平均曲率；高斯曲率；Minkowski Space； Helicoidal Surface； Meaning Curvature； Gauss Curvature
摘要: 三维Minkowski空间中，螺旋面由一条平面曲线进行螺旋运动生成。本文研究以类光向量为轴进行螺旋运动所生成的螺旋面，主要讨论平均曲率H和高斯曲率K满足关系式a1H2 + a2K = g(s)的螺旋面的存在性以及表达式。
Abstract: A helicoidal surface in Minkowski 3-sapce is defined as the orbit of a plane curve under a screw motion. In this paper, we study a kind of helicoidal surface with light-like axis in Minkowski 3-space. As a result, we constructed the representation formulas for these helicoidal surfaces with meaning curvature H and Guass curvature K satisfying a1H2 + a2K = g(s).
文章引用：吴珩, 黄平亮. 三维Minkowski空间中的一类螺旋面[J]. 理论数学, 2015, 5(4): 136-142. http://dx.doi.org/10.12677/PM.2015.54021

参考文献

[1] Naber, G.L. (1992) The geometry of Minkowski Spacetime. Springer-Verlag, New York.
[2] Nappi, J. and Yoshida, H. (2007) Fully automated three-dimensional detection of polyps in fecal-tagging CT colonography. Academic Radiology, 14, 287-300. http://dx.doi.org/10.1016/j.acra.2006.11.007
[3] Balgetir, H., Bektas, M. and Inoguchi, J.I. (2004) Null Bertrand curves in minkowski 3-space and their charaterization. Note di Mathematica, 23, 7-13.
[4] Young, H.K. and Dae, W.Y. (2003) Classification of ruled surfaces in Minkowski 3-spaces. Journal of Geometry and physics, 49, 89-100.
[5] Choi, M., Kim, Y.H. and Yoon, D.W. (2013) Some classification of surfaces of revolution in Minkowski 3-space. Journal of Geometry, 104, 85-106. http://dx.doi.org/10.1007/s00022-013-0149-3
[6] Dillen, F. and Kuhnel, W. (1999) Ruled Weingarten surfaces in Minkowski 3-space. Manuscripta Mathematica, 98, 307-320. http://dx.doi.org/10.1007/s002290050142
[7] Rafael, L. and Esma, D. (2014) Helicoidal surfaces in Minkowski space with constant mean curvature and constant Gauss curvature. Central European Journal of Mathematics, 12, 1349-1361.
[8] Beneki, C.C., Kaimakamis, G. and Papantoniou, B.J. (2002) Helicoidal surface in three dimensional Minkowski space. Journal of Mathematical Analysis and Applications, 275, 586-614. http://dx.doi.org/10.1016/S0022-247X(02)00269-X
[9] Beneki, C.C., Kaimakamis, G. and Papantoniou, B.J. (1998) A classification of surfaces of revolution with constant Guass curvature in 3-dimensiona Minkowski space. Bulletin of the Calcutta Mathematical Society, 90, 441-458.
[10] Hou, Z.H. and Ji, F.H. (2007) Helicoidal surfaces with in Minkowski 3-space. Journal of Mathematical Analysis and Applications, 325, 101-113. http://dx.doi.org/10.1016/j.jmaa.2006.01.017
[11] Ji, F.H. and Hou, Z.H. (2005) A kind of helicoidal surfaces in 3-dimensional Minkowski space. Journal of Mathematical Analysis and Applications, 304, 632-643. http://dx.doi.org/10.1016/j.jmaa.2004.09.065

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