scholarly journals On Special Kinds of Involute and Evolute Curves in 4-Dimensional Minkowski Space

Symmetry ◽  
2018 ◽  
Vol 10 (8) ◽  
pp. 317 ◽  
Author(s):  
Muhammad Hanif ◽  
Zhong Hou ◽  
Kottakkaran Nisar
Keyword(s):  
Minkowski Space ◽  
Vector Fields ◽  
Special Kind ◽  
Advanced Level ◽  
Normal Plane ◽  
Minkowski Space Time ◽  
Dimensional Minkowski Space ◽  
Necessary And Sufficient ◽  
Involute Curve ◽  
The Given

Recently, extensive research has been done on evolute curves in Minkowski space-time. However, the special characteristics of curves demand advanced level observations that are lacking in existing well-known literature. In this study, a special kind of generalized evolute and involute curve is considered in four-dimensional Minkowski space. We consider (1,3)-evolute curves with respect to the casual characteristics of the (1,3)-normal plane that are spanned by the principal normal and the second binormal of the vector fields and the (0,2)-evolute curve that is spanned by the tangent and first binormal of the given curve. We restrict our investigation of (1,3)-evolute curves to the (1,3)-normal plane in four-dimensional Minkowski space. This research contribution obtains a necessary and sufficient condition for the curve possessing the generalized evolute as well as the involute curve. Furthermore, the Cartan null curve is also discussed in detail.

scholarly journals Generalized Timelike Mannheim Curves in Minkowski Space-Time

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
M. Akyig~it ◽  
S. Ersoy ◽  
İ. Özgür ◽  
M. Tosun
Keyword(s):  
Minkowski Space ◽  
Sufficient Conditions ◽  
Space Time ◽  
Necessary And Sufficient Conditions ◽  
Minkowski Space Time ◽  
Mannheim Curve ◽  
Definition Of ◽  
Necessary And Sufficient

We give the definition of generalized timelike Mannheim curve in Minkowski space-time . The necessary and sufficient conditions for the generalized timelike Mannheim curve are obtained. We show some characterizations of generalized Mannheim curve.

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.

scholarly journals Thermal Casimir effect for rectangular cavities inside (D+1)-dimensional Minkowski space–time revisited

2014 ◽  
Vol 29 (08) ◽  
pp. 1450043 ◽  
Author(s):  
Rui-Hui Lin ◽  
Xiang-Hua Zhai
Keyword(s):  
Free Energy ◽  
High Temperature ◽  
Boundary Conditions ◽  
Minkowski Space ◽  
Casimir Effect ◽  
Side Length ◽  
Temperature Dependent ◽  
Dependent Part ◽  
Minkowski Space Time ◽  
Dimensional Minkowski Space

We reconsider the thermal scalar Casimir effect for p-dimensional rectangular cavity inside (D+1)-dimensional Minkowski space–time and clarify the ambiguity in the regularization of the temperature-dependent part of the free energy. We derive rigorously the regularization of the temperature-dependent part of the free energy by making use of the Abel–Plana formula repeatedly and get the explicit expression of the terms to be subtracted. In the cases of D = 3, p = 1 and D = 3, p = 3, we precisely recover the results of parallel plates and three-dimensional box in the literature. Furthermore, for D>p and D = p cases with periodic, Dirichlet and Neumann boundary conditions, we give the explicit expressions of the Casimir free energy in both low temperature (small separations) and high temperature (large separations) regimes, through which the asymptotic behavior of the free energy changing with temperature and the side length is easy to see. We find that for D>p, with the side length going to infinity, the Casimir free energy tends to positive or negative constants or zero, depending on the boundary conditions. But for D = p, the leading term of the Casimir free energy for all three boundary conditions is a logarithmic function of the side length. We also discuss the thermal Casimir force changing with temperature and the side length in different cases and find that when the side length goes to infinity, the force always tends to be zero for different boundary conditions regardless of D>p or D = p. The Casimir free energy and force at high temperature limit behave asymptotically alike that they are proportional to the temperature, be they positive (repulsive) or negative (attractive) in different cases. Our study may be helpful in providing a comprehensive and complete understanding of this old problem.

scholarly journals A New Method for Inextensible Flows of Timelike Curves in Minkowski Space-Time E14

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Talat Körpinar
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Minkowski Space ◽  
Space Time ◽  
New Method ◽  
Frenet Frame ◽  
Partial Differential ◽  
Minkowski Space Time ◽  
Inextensible Flows ◽  
The Given

We construct a new method for inextensible flows of timelike curves in Minkowski space-time E14. Using the Frenet frame of the given curve, we present partial differential equations. We give some characterizations for curvatures of a timelike curve in Minkowski space-time E14.

scholarly journals Spacelike and timelike normal curves in Minkowski space-time

2009 ◽  
Vol 85 (99) ◽  
pp. 111-118 ◽  
Author(s):  
Kazim İlarslan ◽  
Emilija Nesovic
Keyword(s):  
Minkowski Space ◽  
Vector Fields ◽  
Space Time ◽  
Null Vector ◽  
Frenet Frame ◽  
Explicit Equation ◽  
Minkowski Space Time

We define normal curves in Minkowski space-time E41. In particular, we characterize the spacelike normal curves in E41 whose Frenet frame contains only non-null vector fields, as well as the timelike normal curves in E41 , in terms of their curvature functions. Moreover, we obtain an explicit equation of such normal curves with constant curvatures.

On k-Type 2-Degenerate Slant Helices in 4-Dimensional Minkowski Space-Time

2018 ◽  
Vol 7 (1) ◽  
pp. 147-151 ◽  
Author(s):  
Zühal Küçükarslan Yüzbaşı ◽  
Münevver Yıldırım Yılmaz
Keyword(s):  
Minkowski Space ◽  
Space Time ◽  
Minkowski Space Time ◽  
Dimensional Minkowski Space

HOW SINGULAR A SPACE CAN SUPERSTRINGS THREAD?

1991 ◽  
Vol 06 (03) ◽  
pp. 207-216 ◽  
Author(s):  
TRISTAN HÜBSCH
Keyword(s):  
Minkowski Space ◽  
Moduli Space ◽  
Space Time ◽  
3 Dimensional ◽  
Ricci Flat ◽  
Minkowski Space Time ◽  
Dimensional Minkowski Space

Many superstring models with N=1 supergravity in 4-dimensional Minkowski space-time involve σ-models with complex 3-dimensional, Ricci-flat target manifolds. In general, inclusion of singular target spaces probes the boundary of the moduli space and completes it. Studying suitably singular σ-models, the author found certain criteria for the severity of admissible singularizations.

scholarly journals (N, p, q) HARMONIC SUPERSPACE

1995 ◽  
Vol 10 (27) ◽  
pp. 3901-3919 ◽  
Author(s):  
G.G. HARTWELL ◽  
P.S. HOWE
Keyword(s):  
Minkowski Space ◽  
Space Time ◽  
Harmonic Superspace ◽  
Curved Space ◽  
Yang Mills ◽  
Invariant Integrals ◽  
Minkowski Space Time ◽  
Dimensional Minkowski Space ◽  
Harmonic Superspaces ◽  
Super Yang Mills Theory

A family of harmonic superspaces associated with four-dimensional Minkowski space-time is described. Applications are made to free massless supermultiplets, invariant integrals and super-Yang-Mills theory. Generalization to curved space-times is performed, with emphasis on conformal supergravities.

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