SIMILAR AND SELF-SIMILAR CURVES IN MINKOWSKI n-SPACE

다국어 초록 (Multilingual Abstract)

In this paper, we investigate the similarity transformations in the Minkowski n-space. We study the geometric invariants of nonnull curves under the similarity transformations. Besides, we extend the fundamental theorem for a non-null curve according to a similarity motion of En1 . We determine the parametrizations of non-null self-similar curves in En1 .

참고문헌 (Reference)

1 M. F. Barnsley, "V-variable fractals: Fractals with partial self similarity" 218 (218): 2051-2088, 2008

2 B. B. Mandelbrot, "The Fractal Geometry of Nature" W. H. Freeman 1982

3 S. Z. Li, "Similarity invariants for 3D space curve matching" 454-457, 1993

4 R. Encheva, "Similar Frenet curves" 55 (55): 359-372, 2009

5 R. Encheva, "Shapes of space curves" 7 (7): 145-155, 2003

6 B. O'Neill, "Semi-Riemannian Geometry" Academic Press Inc 1983

7 V. Nekrashevych, "Self-similar groups and their geometry" 1 (1): 41-95, 2007

8 R. Grigorchuk, "Self Similarity an branching group theory, Volume 1" Groups St Andrews 2005

9 Q. Ding, "Schrodinger flows, binormal motion for curves and the second AKNS-hierarchies" 21 (21): 669-677, 2004

10 M. Ozdemir, "On the focal curvatures of non-lightlike curves in Minkowski (m+1)-space" 16 (16): 401-409, 2004

11 A. Brook, "On similarity-invariant fairness measures" 3459 : 456-467, 2005

12 A. Ferrandez, "Null helices in Lorentzian space forms" 16 : 4845-4863, 2001

13 D. A. Singer, "Normal forms in Lorentzian spaces" 3 (3): 1-9, 1994

14 K.-S. Chou, "Motions of curves in similarity geometries and Burgers-mKdV hierarchies" 19 (19): 47-53, 2004

15 M. Gurses, "Motion of curves on two-dimensional surfaces and soliton equations" 241 (241): 329-334, 1998

16 K. Nakayama, "Motion of curves in hyperboloid in the Minkowski space" 67 (67): 3031-3037, 1998

17 Y. Kamishima, "Lorentzian similarity manifolds" 10 (10): 1771-1788, 2012

18 W. Greub, "Linear Algebra" Springer Verlag 1967

19 A. Bejancu, "Lightlike curves in Lorentz manifolds" 44 (44): 145-155, 1994

20 K. L. Duggal, "Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications" Kluwer Academic Publishers Group 1996

21 H. Sahbi, "Kernel PCA for similarity invariant shape recognition" 70 : 3034-3045, 2007

22 M. F. Barnsley, "Iterated function systems and the global construction of fractals" 399 (399): 243-275, 1985

23 S. Z. Li, "Invariant representation, matching and pose estimation of 3D space curves under similarity transformation" 30 (30): 447-458, 1997

24 K.-S. Chou, "Integrable equations arising from motions of plane curves" 162 (162): 9-33, 2002

25 M. Berger, "Geometry I" Springer 1987

26 J. E. Hutchinson, "Fractals and self-similarity" 30 (30): 713-747, 1981

27 K. Falconer, "Fractal Geometry" John Wiley & Sons, Ltd 2003

28 J. G. Alcazar, "Detecting similarity of rational plane curves" 269 : 1-13, 2014

29 T. Aristide, "Closed similarity Lorentzian Affne manifolds" 132 (132): 3697-3702, 2004

30 D. Xu, "3-D curve moment invariants for curve recognition" 345 : 572-577, 2006