On translation surfaces in 4-dimensional Euclidean space

被引：15

作者：

Arslan, Kadri ^{[1
]}

Bayram, Bengu ^{[2
]}

Bulca, Betul ^{[1
]}

Ozturk, Gunay ^{[3
]}

机构：

[1] Uludag Univ, Art & Sci Fac, Dept Math, Bursa, Turkey

[2] Balikesir Univ, Art & Sci Fac, Dept Math, Balikesir, Turkey

[3] Kocaeli Univ, Art & Sci Fac, Dept Math, TR-41380 Kocaeli, Turkey

来源：

ACTA ET COMMENTATIONES UNIVERSITATIS TARTUENSIS DE MATHEMATICA | 2016年 / 20卷 / 02期

关键词：

Translation surface; mean curvature; Gaussian curvature; second fundamental map;

D O I：

10.12697/ACUTM.2016.20.11

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider translation surfaces in Euclidean spaces. Firstly, we give some results of translation surfaces in the 3-dimensional Euclidean space E-3. Further, we consider translation surfaces in the 4-dimensional Euclidean space E-4. We prove that a translation surface is flat in E-4 if and only if it is either a hyperplane or a hypercylinder. Finally we give necessary and sufficient condition for a quadratic triangular Bezier surface in E-4 to become a translation surface.

引用

页码：123 / 133

页数：11

共 50 条

[1] MINIMAL SURFACES OF 4-DIMENSIONAL EUCLIDEAN SPACE
ROSCA, R
[J]. COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES SERIE A, 1970, 270 (10): : 657 - &
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BURES, J
[J]. CZECHOSLOVAK MATHEMATICAL JOURNAL, 1975, 25 (03) : 480 - 490
[4] EXTREME 2-DIMENSIONAL SURFACES IN 4-DIMENSIONAL EUCLIDEAN-SPACE
BERNIK, VI
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[J]. ACTA ARITHMETICA, 1990, 53 (04) : 333 - 349
[5] SCREWING IN 4-DIMENSIONAL EUCLIDEAN SPACE
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[J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1976, 285 : 77 - 99
[6] SPACE OF MOMENTS IN THE GEOMETRY OF PAIRS OF RULED SURFACES OF THE 4-DIMENSIONAL EUCLIDEAN-SPACE
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[9] HYPERSURFACES IN 4-DIMENSIONAL EUCLIDEAN-SPACE
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