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

Year 2018, Volume: 11 Issue: 2, 61 - 70, 30.11.2018
https://doi.org/10.36890/iejg.545132

Abstract


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.
Year 2018, Volume: 11 Issue: 2, 61 - 70, 30.11.2018
https://doi.org/10.36890/iejg.545132

Abstract

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.
There are 23 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Hakan Şimşek This is me

Mustafa Özdemir

Publication Date November 30, 2018
Published in Issue Year 2018 Volume: 11 Issue: 2

Cite

APA Şimşek, H., & Özdemir, M. (2018). Some Results on p-Shape Curvatures of Non-Lightlike Space Curves. International Electronic Journal of Geometry, 11(2), 61-70. https://doi.org/10.36890/iejg.545132
AMA Şimşek H, Özdemir M. Some Results on p-Shape Curvatures of Non-Lightlike Space Curves. Int. Electron. J. Geom. November 2018;11(2):61-70. doi:10.36890/iejg.545132
Chicago Şimşek, Hakan, and Mustafa Özdemir. “Some Results on P-Shape Curvatures of Non-Lightlike Space Curves”. International Electronic Journal of Geometry 11, no. 2 (November 2018): 61-70. https://doi.org/10.36890/iejg.545132.
EndNote Şimşek H, Özdemir M (November 1, 2018) Some Results on p-Shape Curvatures of Non-Lightlike Space Curves. International Electronic Journal of Geometry 11 2 61–70.
IEEE H. Şimşek and M. Özdemir, “Some Results on p-Shape Curvatures of Non-Lightlike Space Curves”, Int. Electron. J. Geom., vol. 11, no. 2, pp. 61–70, 2018, doi: 10.36890/iejg.545132.
ISNAD Şimşek, Hakan - Özdemir, Mustafa. “Some Results on P-Shape Curvatures of Non-Lightlike Space Curves”. International Electronic Journal of Geometry 11/2 (November 2018), 61-70. https://doi.org/10.36890/iejg.545132.
JAMA Şimşek H, Özdemir M. Some Results on p-Shape Curvatures of Non-Lightlike Space Curves. Int. Electron. J. Geom. 2018;11:61–70.
MLA Şimşek, Hakan and Mustafa Özdemir. “Some Results on P-Shape Curvatures of Non-Lightlike Space Curves”. International Electronic Journal of Geometry, vol. 11, no. 2, 2018, pp. 61-70, doi:10.36890/iejg.545132.
Vancouver Şimşek H, Özdemir M. Some Results on p-Shape Curvatures of Non-Lightlike Space Curves. Int. Electron. J. Geom. 2018;11(2):61-70.