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 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.

Ruled surfaces of finite type in 3- dimensional minkowski space

1995 ◽  
Vol 27 (3-4) ◽  
pp. 250-255 ◽  
Author(s):  
Franki Dillen ◽  
Leopold Verstraelen ◽  
Ignace Van de Woestyne ◽  
Leopold Verstraelen ◽  
Johan Walrave
Keyword(s):  
Minkowski Space ◽  
Finite Type ◽  
Ruled Surfaces ◽  
3 Dimensional ◽  
Dimensional Minkowski Space

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 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.

scholarly journals Foliations between crooked planes in 3-dimensional Minkowski space

2019 ◽  
Vol 30 (01) ◽  
pp. 1950004
Author(s):  
Jean-Philippe Burelle ◽  
Dominik Francoeur
Keyword(s):  
Minkowski Space ◽  
3 Dimensional ◽  
Dimensional Minkowski Space ◽  
Minkowski Formula

We show that any two disjoint crooked planes in [Formula: see text] are leaves of a crooked foliation. This answers a question asked by Charette and Kim [V. Charette and Y. Kim, Foliations of Minkowski [Formula: see text] spacetime by crooked planes, Int. J. Math. 25(9) (2014) 1450088.].

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