Mappings that preserve helices in the n-dimensional Minkowski spaces

2020 ◽  
Vol 17 (10) ◽  
pp. 2050107
Author(s):  
Bülent Altunkaya
Keyword(s):  
Minkowski Space ◽  
Minkowski Spaces ◽  
Dimensional Minkowski Space

We introduce two types of mappings that preserve nonnull helices in Minkowski spaces. The first type constructs helices in the [Formula: see text]-dimensional Minkowski space from helices in the same Minkowski space. The second type constructs helices in the [Formula: see text]-dimensional Minkowski space from helices in the [Formula: see text]-dimensional Minkowski space. Furthermore, we study invariants of these mappings and present examples.

scholarly journals ON NONLINEARITY OF p-BRANE DYNAMICS

2012 ◽  
Vol 09 (06) ◽  
pp. 1261017 ◽  
Author(s):  
A. A. ZHELTUKHIN
Keyword(s):  
Exact Solutions ◽  
Minkowski Space ◽  
Nonlinear Equations ◽  
New Exact Solutions ◽  
Dimensional Minkowski Space

Nonlinear equations of p-branes in D = (2p + 1)-dimensional Minkowski space are discussed. Presented are new exact solutions for a set of spinning p-branes with the Abelian symmetries U(1) × U(1) × ⋯ ×U(1) of their shapes.

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 Elastic shocks in relativistic rigid rods and balls

2019 ◽  
Vol 475 (2225) ◽  
pp. 20180858 ◽  
Author(s):  
João L. Costa ◽  
José Natário
Keyword(s):  
Free Boundary ◽  
Minkowski Space ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Time Derivative ◽  
Space Time ◽  
Spherically Symmetric ◽  
Soft Phase ◽  
Minkowski Space Time ◽  
Dimensional Minkowski Space

We study the free boundary problem for the ‘hard phase’ material introduced by Christodoulou in (Christodoulou 1995 Arch. Ration. Mech. Anal. 130 , 343–400), both for rods in (1 + 1)-dimensional Minkowski space–time and for spherically symmetric balls in (3 + 1)-dimensional Minkowski space–time. Unlike Christodoulou, we do not consider a ‘soft phase’, and so we regard this material as an elastic medium, capable of both compression and stretching. We prove that shocks must be null hypersurfaces, and derive the conditions to be satisfied at a free boundary. We solve the equations of motion of the rods explicitly, and we prove existence of solutions to the equations of motion of the spherically symmetric balls for an arbitrarily long (but finite) time, given initial conditions sufficiently close to those for the relaxed ball at rest. In both cases we find that the solutions contain shocks if and only if the pressure or its time derivative do not vanish at the free boundary initially. These shocks interact with the free boundary, causing it to lose regularity.

The two-dimensional minkowski space fermion determinant by example

1988 ◽  
Vol 211 (1-2) ◽  
pp. 107-110 ◽  
Author(s):  
D. Cangemi ◽  
M. Makowka ◽  
G. Wanders
Keyword(s):  
Minkowski Space ◽  
Two Dimensional ◽  
Dimensional Minkowski Space

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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