三维欧氏空间的仿射乘积曲面

宗鹏, 肖琳, 刘会立

数学学报 ›› 2015, Vol. 58 ›› Issue (2) : 329-336.

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数学学报 ›› 2015, Vol. 58 ›› Issue (2) : 329-336. DOI: 10.12386/A2015sxxb0032
论文

三维欧氏空间的仿射乘积曲面

    宗鹏1,2, 肖琳3, 刘会立3
作者信息 +

Affine Factorable Surfaces in Three-Dimensional Euclidean Space

    Peng ZONG1,2, Lin XIAO3, Hui Li LIU3
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文章历史 +

摘要

定义了三维欧氏空间中的仿射乘积曲面,给出了极小仿射乘积曲面以及高斯曲率为零的仿射乘积曲面的分类,同时还给出了平均曲率为非零常数的仿射乘积曲面的分类.

Abstract

Affine factorable surfaces in Euclidean 3-space were defined. The classification of surfaces with zero Gauss curvature and nonzero constant mean curvature and minimal affine factorable surfaces was given.

关键词

仿射乘积曲面 / 平均曲率 / 高斯曲率

Key words

affine factorable surface / mean curvature / Gauss curvature

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导出引用
宗鹏, 肖琳, 刘会立. 三维欧氏空间的仿射乘积曲面. 数学学报, 2015, 58(2): 329-336 https://doi.org/10.12386/A2015sxxb0032
Peng ZONG, Lin XIAO, Hui Li LIU. Affine Factorable Surfaces in Three-Dimensional Euclidean Space. Acta Mathematica Sinica, Chinese Series, 2015, 58(2): 329-336 https://doi.org/10.12386/A2015sxxb0032

参考文献

[1] Deng Y. J., Liu H. L., Rotation surfaces with constant mean curvature in 3-dimensional Anti-de Sitter space, Acta Mathematica Sinica, Chinese Series, 2002, 45(6): 1178-1184.

[2] Liu H. L., Translation surfaces with dependent Gaussian and mean curvature in 3-dimensional spaces, J. North. Instit. Techn., 1993, 14(1): 88-93.

[3] Liu H. L., Yu Y. H., Affine translation surfaces in Euclidean 3-space, Proc. Japan Academy, Math. Sci., Ser. A, 2013, 89: 111-113.

[4] Meng H. H., Liu H. L., Factorable Surfaces in 3-Minkowski space, Bull. Korean Math. Soc., 2009, 46(1): 155-169.

[5] Mohammed B., Bendehiba S., Factorable surfaces in the three dimensional Euclidean and Lorentzian spaces satisfying Δri = λiRi, J. Geom., 2012, 103(1): 17-29.

[6] Verstraelen L., Walrave J., Yaprak S., The minimal translation surfaces in Euclidean space, Soochow J. Math., 1994, 20(1): 77-82.

[7] Yang Y., Yu Y. H., Liu H. L., Revolution surfaces with given mean curvature in 3-D Minkowski space, J. North. Univ.: Natural Science, 2012, 33(9): 1361-1368 (in Chinese).

[8] Yu Y. H., Liu H. L., Seoung D. J., Structure and characterization of ruled surfaces in Euclidean space, Appl. Math. Comput., 2014, 233(1): 252-259.

[9] Yu Y. H., Yang Y., Liu H. L., Centroaffine ruled surfaces in R3, J. Mathe. Anal. Appl., 2010, 365(2): 683-693.

[10] Yuan Y., Ma L. B., Liu H. L., Affine translation surfaces in Minkowski 3D-space, J. North. Univ.: Natural Science, 2013, 34(10): 1518-1520 (in Chinese).

基金

国家自然科学基金资助项目(11371080)

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