Classifications of Flat Surfaces with Generalized 1-Type Gauss Map in L3

被引：0

作者：

Yoon, Dae Won ^{[1
,2
]}

Kim, Dong-Soo ^{[3
]}

Kim, Young Ho ^{[4
]}

Lee, Jae Won ^{[1
,2
]}

机构：

[1] Gyeongsang Natl Univ, Dept Math, Jinju 52828, South Korea

[2] Gyeongsang Natl Univ, RINS, Jinju 52828, South Korea

[3] Chonnam Natl Univ, Dept Math, Gwangju 61186, South Korea

[4] Kyungpook Natl Univ, Dept Math, Daegu 41566, South Korea

来源：

MEDITERRANEAN JOURNAL OF MATHEMATICS | 2018年 / 15卷 / 03期

基金：

新加坡国家研究基金会;

关键词：

Developable surface; Generalized 1-type Gauss map; Null scroll; RULED SURFACES; ROTATIONAL SURFACES; REVOLUTION; HYPERSURFACES; SUBMANIFOLDS; E-4;

D O I：

10.1007/s00009-018-1123-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study surfaces in the Minkowski 3-space L-3, such that Delta G is a linear combination of the Gauss map G and a constant vector C, called generalized 1-type Gauss map. First of all, we prove that all cylindrical surfaces in L-3 have generalized 1-type Gauss map. Second, we classify conical surfaces with generalized 1-type Gauss map in L-3. After then, nonplanar tangent developable surfaces in the Minkowski 3-space L-3 with generalized 1-type Gauss map are open pieces of a Euclidean plane or a Minkowski plane. Finally, we show that a null scroll in the Minkowski 3-space L-3 has generalized 1-type Gauss map if and only if it is either an open piece of a Minkowski plane or a B-scroll.

引用

页数：16

共 25 条

[1] BOOST INVARIANT SURFACES WITH POINTWISE 1-TYPE GAUSS MAP IN MINKOWSKI 4-SPACE E14 [J].