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DIFFERENTIAL EQUATIONS CHARACTERIZING TIMELIKE AND SPACELIKE CURVES OF CONSTANT BREADTH IN MINKOWSKI 3-SPACE E13
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 Title & Authors
DIFFERENTIAL EQUATIONS CHARACTERIZING TIMELIKE AND SPACELIKE CURVES OF CONSTANT BREADTH IN MINKOWSKI 3-SPACE E13
Onder, Mehmet; Kocayigit, Huseyin; Canda, Elif;
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 Abstract
In this paper, we give the differential equations characterizing the timelike and spacelike curves of constant breadth in Minkowski 3-space . Furthermore, we give a criterion for a timelike or spacelike curve to be the curve of constant breadth in . As an example, the obtained results are applied to the case = const. and = const., and are discussed.
 Keywords
Minkowski 3-space;timelike curve;spacelike curve;constant breadth curve;
 Language
English
 Cited by
1.
On Closed Space Curves in Minkowski Space–Time $${E_v^n}$$, Differential Equations and Dynamical Systems, 2012, 20, 2, 179  crossref(new windwow)
 References
1.
N. H. Ball, On Ovals, Amer. Math. Monthly 37 (1930), no. 7, 348-353. crossref(new window)

2.
E. Barbier, J. de Math. 2 (1860), no. 5, 272-286.

3.
W. Blaschke, Konvexe Bereiche gegebener konstanter Breite und kleinsten Inhalts, Math. Ann. 76 (1915), no. 4, 504-513. crossref(new window)

4.
W. Blaschke, Leibziger Berichte, 67 (1917), p. 290.

5.
S. Breuer and D. Gottlieb, The Reduction of Linear Ordinary Differential Equations to Equations with Constant Coefficients, J. Math. Anal. Appl. 32 (1970), no. 1, 62-76. crossref(new window)

6.
H. C. Chung, A differential-geometric criterion for a space curve to be closed, Proc. Amer. Math. Soc. 83 (1981), no. 2, 357-361. crossref(new window)

7.
L. Euler, De curvis triangularibus, Acta Acad. Prtropol. (1778), (1780), 3-30.

8.
M. Fujivara, On space curves of constant breadth, Tohoku Math. J. 5 (1914), 179-784.

9.
M. Kazaz, M. Onder, and H. Kocayit, Spacelike curves of constant breadth in Minkowski 4-space, Int. J. Math. Anal. (Ruse) 2 (2008), no. 21-24, 1061-1068.

10.
O. Kose, On space curves of constant breadth, Doga Mat. 10 (1986), no. 1, 11-14.

11.
A. Maden and O. Kose, On the curves of constant breadth in $E^4$ space, Turkish J. Math. 21 (1997), no. 3, 277-284.

12.
A. P. Mellish, Notes on differential geometry, Ann. of Math. (2) 32 (1931), no. 1, 181- 190. crossref(new window)

13.
B. O'Neil, Semi-Riemannian Geometry with Applications to Relativity, Academic Press, New York, 1983.

14.
F. Reuleaux, The Kinematics of Machinery, Trans. By A. B. W. Kennedy, Dover, Pub. Nex York, 1963.

15.
S. L. Ross, Differential Equations, John Wiley and Sons, Inc., New York, 1974.

16.
M. Sezer, Differential equations characterizing space curves of constant breadth and a criterion for these curves, Doga Mat. 13 (1989), no. 2, 70-78.

17.
S. Smakal, Curves of constant breadth, Czechoslovak Math. J. 23(98) (1973), 86-94.

18.
D. J. Struik, Differential geometry in the large, Bull. Amer. Math. Soc. 37 (1931), no. 2, 49-62. crossref(new window)

19.
H. Tanaka, Kinematics Design of Com Follower Systems, Doctoral Thesis, Columbia Univ., 1976.

20.
J. Walrave, Curves and Surfaces in Minkowski Space, Doctoral Thesis, K. U. Leuven, Faculty of Sciences, Leuven, 1995.