Some Results on p-Shape Curvatures of Non-Lightlike Space Curves

Year 2018, , 61 - 70, 30.11.2018

Hakan Şimşek Mustafa Özdemir

https://doi.org/10.36890/iejg.545132

Abstract

Keywords

p-shape curvature, p-similarity, helix

References

• [1] Alcázar, J. G., Hermosoa, C. and Muntingh, G., Detecting similarity of rational plane curves, Journal of Computational and Applied Mathematics, 269 (2014), 1–13.
• [2] Ali, A. T. and Lopez, R., Slant Helices in Minkowski Space E31, J. Korean Math. Soc. 48 (2011), 159-167.
• [3] Babaarslan, M. and Yaylı, Y., Time-Like Constant Slope Surfaces and Space-Like Bertrand Curves in Minkowski 3-Space, Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci., 84 (2014), 535–540.
• [4] Barnsley, M. F., Hutchinson, J. E. and Stenflo, Ö., V-variable fractals: Fractals with partial self similarity, Advances in Mathematics, 218 (2008), 2051-2088.
• [5] Berger, M., Geometry I. Springer, New York, 1998.
• [6] Brook, A., Bruckstein, A. M. and Kimmel, R., On Similarity-Invariant Fairness Measures, LNCS, 3459 (2005), 456–467.
• [7] Encheva, R. and Georgiev, G., Shapes of space curves, J. Geom. Graph., 7 (2003), 145-155.
• [8] Encheva, R. and Georgiev, G., Similar Frenet curves, Results in Mathematics, 55 (2009), 359–372.
• [9] Hutchinson, J. E., Fractals and Self-Similarity, Indiana University Mathematics Journal, 30 (1981), N:5.
• [10] K. Falconer, K., Fractal Geometry: Mathematical Foundations and Applications, Second Edition, John Wiley & Sons, Ltd., 2003.
• [11] Inoguchi, J., Biharmonic curves in Minkowski 3-space, International Journal of Mathematics and Mathematical Sciences, 21 (2003), 1365-1368.
• [12] Izumiya, S., Pei, D., Sano, T. and Torii E., Evolutes of Hyperbolic Plane Curves, Acta Mathematica Sinica, English Series, 20 (2004), 543–550.
• [13] Izumiya, S. and Takeuchi, N., Generic properties of helices and Bertrand curves, J. Geom., 74 (2002), 97-109.
• [14] Izumiya, S. and Takeuchi, N., New special curves and developable surfaces, Turkish J. Math., 28 (2004), 153-163.
• [15] Li, S. Z., Invariant Representation, Matching and Pose Estimation of 3D Space Curves Under Similarity Transformation, Pattern Recognition, 30 (1997), 447-458.
• [16] Li, S. Z., Similarity Invariants for 3D Space Curve Matching, In Proceedings of the First Asian Conference on Computer Vision, Japan (1993), 454-457.
• [17] López, R., Differential Geometry of Curves and Surfaces in Lorentz-Minkowski Space, International Electronic Journal of Geometry, 7 (2014), 44-107.
• [18] Mandelbrot, B. B., The Fractal Geometry of Nature, New York: W. H. Freeman, 1983.
• [19] O’Neill, B., Semi-Riemannian Geometry with Applications to Relativity, Academic Press Inc., London, 1983.
• [20] Özdemir, M., Ergin, A. A., Rotations with unit timelike quaternions in Minkowski 3-space, Journal of Geometry and Physics, 56 (2006), 322–336.
• [21] Özdemir, M., Ergin, A. A., Spacelike Darboux Curves in Minkowski 3-Space, Differ. Geom. Dyn. Syst., 9 (2007), 131-137.
• [22] Sahbi, H., Kernel PCA for similarity invariant shape recognition, Neurocomputing, 70 (2007), 3034–3045.
• [23] Şimşek, H. and Özdemir, M., Similar and Self-Similar Curves in Minkowski n-Space, B. Korean Math. Soc., 52 (2015), 2071–2093.