scholarly journals Prescribing Gauss curvature of surfaces in 3-dimensional spacetimes Application to the Minkowski problem in the Minkowski space

2011 ◽  
Vol 61 (2) ◽  
pp. 511-591 ◽  
Author(s):  
Thierry Barbot ◽  
François Béguin ◽  
Abdelghani Zeghib
Keyword(s):  
Minkowski Space ◽  
Gauss Curvature ◽  
Minkowski Problem ◽  
3 Dimensional

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.].

scholarly journals Helicoidal surfaces in Minkowski space with constant mean curvature and constant Gauss curvature

2014 ◽  
Vol 12 (9) ◽  
Author(s):  
Rafael López ◽  
Esma Demir
Keyword(s):  
Minkowski Space ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Gauss Curvature ◽  
First Case ◽  
Helicoidal Surfaces ◽  
Constant Gauss Curvature

AbstractWe classify all helicoidal non-degenerate surfaces in Minkowski space with constant mean curvature whose generating curve is a the graph of a polynomial or a Lorentzian circle. In the first case, we prove that the degree of the polynomial is 0 or 1 and that the surface is ruled. If the generating curve is a Lorentzian circle, we prove that the only possibility is that the axis is spacelike and the center of the circle lies on the axis.

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