Invariants of non-developable ruled surfaces in Euclidean 3-space

被引：12

作者：

Liu, Huili ^{[1
]}

Yu, Yanhua ^{[1
]}

Dal Jung, Seoung ^{[2
]}

机构：

[1] Northeastern Univ, Dept Math, Shenyang 110004, Liaoning, Peoples R China

[2] Jeju Natl Univ, Dept Math, Jeju 690756, South Korea

来源：

BEITRAGE ZUR ALGEBRA UND GEOMETRIE-CONTRIBUTIONS TO ALGEBRA AND GEOMETRY | 2014年 / 55卷 / 01期

关键词：

Spherical curve; Frenet formula; Ruled surface; Structure function; Pitch function; Angle function of pitch; Center of torsion;

D O I：

10.1007/s13366-013-0177-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, using the classical methods of differential geometry, we define invariants of non-developable ruled surfaces in Euclidean 3-space, called structure functions, and show kinematics meaning of these invariants. We also generalize the notion of the angle of pitch of a closed ruled surface to any non-developable ruled surface. Then we discuss the properties of these invariants and give a kind of classification of the non-developable ruled surfaces in Euclidean 3-space with the theories of these invariants.

引用

页码：189 / 199

页数：11

共 44 条

[31] ON TIMELIKE PARALLEL p(i)-EQUIDISTANT RULED SURFACES WITH A SPACELIKE BASE CURVE IN THE MINKOWSKI 3-SPACE R-1(3) [J].

Masal, Melek ;

Kuruoglu, Nuri .

INTERNATIONAL ELECTRONIC JOURNAL OF GEOMETRY, 2011, 4 (01) :26-31

[32] On Timelike Parallel p(i)-Equidistant Ruled Surfaces with a Timelike Base Curve in the Minkowski 3-Space R-1(3) [J].

Masal, Melek ;

Kuruoglu, Nuri .

BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA, 2015, 33 (02) :133-141

[33] Classification of Ruled Surfaces as Homothetic Self-Similar Solutions of the Inverse Mean Curvature Flow in the Lorentz–Minkowski 3-Space [J].

Gregório Silva ;

Vanessa Silva .

Bulletin of the Brazilian Mathematical Society, New Series, 2023, 54

[34] On the Gauss map of translation surfaces in Minkowski 3-space [J].

Yoon, DW .

TAIWANESE JOURNAL OF MATHEMATICS, 2002, 6 (03) :389-398

[35] Classification of Ruled Surfaces as Homothetic Self-Similar Solutions of the Inverse Mean Curvature Flow in the Lorentz-Minkowski 3-Space [J].

Neto, Gregorio Silva ;

Silva, Vanessa .

BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, 2023, 54 (04)

[36] Ruled surfaces with lightlike ruling in 3-Minkowski space [J].

Liu, Huili .

JOURNAL OF GEOMETRY AND PHYSICS, 2009, 59 (01) :74-78

[37] ON INTEGRAL INVARIANTS OF RULED SURFACES GENERATED BY THE DARBOUX FRAMES OF THE TRANSVERSAL INTERSECTION CURVE OF TWO SURFACES IN E-3 [J].

As, Engin ;

Sarioglugil, Ayhan .

JOURNAL OF SCIENCE AND ARTS, 2016, (02) :111-128

[38] Certain Constant Angle Surfaces Constructed on Curves in Minkowski 3-Space [J].

Karakus, Siddika Ozkaldi .

INTERNATIONAL ELECTRONIC JOURNAL OF GEOMETRY, 2018, 11 (01) :37-47

[39] Surface Pencil Pair Interpolating Bertrand Pair as Common Asymptotic Curves in Euclidean 3-Space [J].

Mofarreh, Fatemah ;

Abdel-Baky, Rashad A. .

MATHEMATICS, 2023, 11 (16)

[40] Surface family pair with Bertrand pair as mutual geodesic curves in Euclidean 3-space E3 [J].

Almoneef, Areej A. ;

Abdel-Baky, Rashad A. .

AIMS MATHEMATICS, 2023, 8 (09) :20546-20560

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