scholarly journals On the Gauss Map of Surfaces of Revolution with Nonlightlike Axis in Minkowski 3-Space

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Minghao Jin ◽  
Donghe Pei
Keyword(s):  
Minkowski Space ◽  
Classification Problem ◽  
Gauss Map ◽  
Real Matrix ◽  
Surfaces Of Revolution ◽  
3 Dimensional ◽  
Dimensional Minkowski Space

We study surfaces of revolution with a nonlightlike axis in 3-dimensional Minkowski space and classify such surfaces in terms of the Gauss mapGthat satisfies the conditionΔhG=ΛG, with Λ being a3×3real matrix. Furthermore, this paper completes the classification problem of surfaces of revolution in Minkowski 3-space given by Jin et al. (2013).

scholarly journals On the Gauss Map of Surfaces of Revolution with Lightlike Axis in Minkowski 3-Space

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Minghao Jin ◽  
Donghe Pei ◽  
Shu Xu
Keyword(s):  
Gauss Map ◽  
Second Fundamental Form ◽  
Satisfy Condition ◽  
Real Matrix ◽  
De Sitter ◽  
Surfaces Of Revolution ◽  
3 Dimensional ◽  
The Second Fundamental Form ◽  
Dimensional Minkowski Space ◽  
Lightlike Axis

By studying the Gauss mapGand Laplace operatorΔhof the second fundamental formh, we will classify surfaces of revolution with a lightlike axis in 3-dimensional Minkowski space and also obtain the surface of Enneper of the 2nd kind, the surface of Enneper of the 3rd kind, the de Sitter pseudosphere, and the hyperbolic pseudosphere that satisfy conditionΔhG=ΛG, Λbeing a3×3real matrix.

scholarly journals Classification Theorems in Minkowski 3-space

2018 ◽  
Author(s):  
Miekyung Choi ◽  
Young Ho Kim
Keyword(s):  
Minkowski Space ◽  
Gauss Map ◽  
Ruled Surfaces ◽  
3 Dimensional ◽  
Dimensional Minkowski Space

By generalizing the notion of pointwise 1-type Gauss map, the generalized 1-type Gauss map has been recently introduced. Without any assumption, we classified all possible ruled surfaces with generalized 1-type Gauss map in a 3-dimensional Minkowski space. In particular, null scrolls do not have the proper generalized 1-type Gauss map. In fact, it is harmonic.

scholarly journals Classification Theorems of Ruled Surfaces in Minkowski Three-Space

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 318
Author(s):  
Miekyung Choi ◽  
Young Kim
Keyword(s):  
Minkowski Space ◽  
Gauss Map ◽  
Ruled Surfaces ◽  
3 Dimensional ◽  
Dimensional Minkowski Space ◽  
Three Space

By generalizing the notion of the pointwise 1-type Gauss map, the generalized 1-type Gauss map has been recently introduced. Without any assumption, we classified all possible ruled surfaces with the generalized 1-type Gauss map in a 3-dimensional Minkowski space. In particular, null scrolls do not have the proper generalized 1-type Gauss map. In fact, it is harmonic.

scholarly journals New Representations of Spherical Indicatricies of Bertrand Curves in Minkowski 3-Space

Geometry ◽  
2015 ◽  
Vol 2015 ◽  
pp. 1-5
Author(s):  
İsmail Aydemir ◽  
Fırat Yerlikaya
Keyword(s):  
Minkowski Space ◽  
3 Dimensional ◽  
Bertrand Curve ◽  
Dimensional Minkowski Space ◽  
Characteristic Features

We obtained a new representation for timelike Bertrand curves and their Bertrand mate in 3-dimensional Minkowski space. By using this representation, we expressed new representations of spherical indicatricies of Bertrand curves and computed their curvatures and torsions. Furthermore in case the indicatricies of a Bertrand curve are slant helices, we investigated some new characteristic features of these curves.

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