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ELASTIC CURVES IN A TWO-DIMENSIONAL LIGHTLIKE CONE

Year 2015, , 1 - 8, 30.10.2015
https://doi.org/10.36890/iejg.592272

Abstract

References

  • [1] Barros, M., Ferrndez, A., Lucas, P. and Meroo, M.A., Willmore Tori and Willmore-Chen Submanifolds in Pseudo-Riemannian Spaces,Journal of Geom- etry and Physics, 28(1998), 45-66.
  • [2] Bolza, O., Vorlesungen Ueber Variationsrechnung, Koehler und Amelang, Leipzig, 1949.
  • [3] Brunnett, G., A New Characterization of Plane Elastica, Mathematical Meth- ods in Computer Aided Geometric Design II (eds.) Tom Lyche and Larry L. Schumaker (Academic Press, Inc., 1992), 43-56.
  • [4] Brunnett, G. and Crouch, P.E., Elastic Curves on the Sphere, Naval Postgrad- uate School, Monterey, California, 1993.
  • [5] Huang, R., A Note on the p-elastica in a Constant Sectional Curvature Mani- fold, Journal of Geometry and Physics, 49(2004), 343-349.
  • [6] Langer, J. and Singer, D., The Total Squared Curvature of Closed Curves, Journal of Differential Geometry, 20(1984), 1-22.
  • [7] Liu, H., Curves in the Lightlike Cone, Beitrge zur Algebra und Geometrie Contributions to Algebra and Geometry, 44(2004), no. 1, 291-303.
  • [8] Liu, H., Meng, Q., Representation Formulas of Curves in a two and three- dimensional Lightlike Cone, Results in Mathematics, 59(2011), 437-451.
  • [9] Lopez, R., Differential Geometry of Curves and Surfaces in Lorentz- Minkowski Space, International Electronic Journal of Geometry, 7(2014), no.1, 44-107.
  • [10] O’Neill, B., Semi-Riemannian Geometry with Applications to Relativity, Aca- demic Pres., New York, 1993.
  • [11] Oral, M., Elastic Curves on Hyperquadrics in Minkowski 3-space, Master The- sis, Sleyman Demirel University, Graduate School of Natural and Applied Sci- ences, 2010, 40p.
  • [12] Ozkan, G., Elastic Strips in Minkowski 3-space, Doctoral Thesis, Sleyman Demirel University, Graduate School of Natural and Applied Sciences, 2014, 93p.
  • [13] Singer, D. Lectures on elastic curves and rods, AIP Conf. Proc. 1002, Amer. Inst. Phys., Melville. New York, 2008.
  • [14] Steinberg, D., H., Elastic Curves in Hyperbolic Space, Doctoral Thesis, Case Western Reserve University, UMI Microform 9607925, 1995, 72p.
  • [15] Weinstock, R., Calculus of Variations, McGraw-Hill Book Company, USA, 1952, 326p.
  • [16] Yucesan, A. and Oral, M., Elastica on 2-dimensional anti-De Sitter space, International Journal of Geometric Methods in Modern Physics, 8(2011), no.1, 107-113.
Year 2015, , 1 - 8, 30.10.2015
https://doi.org/10.36890/iejg.592272

Abstract

References

  • [1] Barros, M., Ferrndez, A., Lucas, P. and Meroo, M.A., Willmore Tori and Willmore-Chen Submanifolds in Pseudo-Riemannian Spaces,Journal of Geom- etry and Physics, 28(1998), 45-66.
  • [2] Bolza, O., Vorlesungen Ueber Variationsrechnung, Koehler und Amelang, Leipzig, 1949.
  • [3] Brunnett, G., A New Characterization of Plane Elastica, Mathematical Meth- ods in Computer Aided Geometric Design II (eds.) Tom Lyche and Larry L. Schumaker (Academic Press, Inc., 1992), 43-56.
  • [4] Brunnett, G. and Crouch, P.E., Elastic Curves on the Sphere, Naval Postgrad- uate School, Monterey, California, 1993.
  • [5] Huang, R., A Note on the p-elastica in a Constant Sectional Curvature Mani- fold, Journal of Geometry and Physics, 49(2004), 343-349.
  • [6] Langer, J. and Singer, D., The Total Squared Curvature of Closed Curves, Journal of Differential Geometry, 20(1984), 1-22.
  • [7] Liu, H., Curves in the Lightlike Cone, Beitrge zur Algebra und Geometrie Contributions to Algebra and Geometry, 44(2004), no. 1, 291-303.
  • [8] Liu, H., Meng, Q., Representation Formulas of Curves in a two and three- dimensional Lightlike Cone, Results in Mathematics, 59(2011), 437-451.
  • [9] Lopez, R., Differential Geometry of Curves and Surfaces in Lorentz- Minkowski Space, International Electronic Journal of Geometry, 7(2014), no.1, 44-107.
  • [10] O’Neill, B., Semi-Riemannian Geometry with Applications to Relativity, Aca- demic Pres., New York, 1993.
  • [11] Oral, M., Elastic Curves on Hyperquadrics in Minkowski 3-space, Master The- sis, Sleyman Demirel University, Graduate School of Natural and Applied Sci- ences, 2010, 40p.
  • [12] Ozkan, G., Elastic Strips in Minkowski 3-space, Doctoral Thesis, Sleyman Demirel University, Graduate School of Natural and Applied Sciences, 2014, 93p.
  • [13] Singer, D. Lectures on elastic curves and rods, AIP Conf. Proc. 1002, Amer. Inst. Phys., Melville. New York, 2008.
  • [14] Steinberg, D., H., Elastic Curves in Hyperbolic Space, Doctoral Thesis, Case Western Reserve University, UMI Microform 9607925, 1995, 72p.
  • [15] Weinstock, R., Calculus of Variations, McGraw-Hill Book Company, USA, 1952, 326p.
  • [16] Yucesan, A. and Oral, M., Elastica on 2-dimensional anti-De Sitter space, International Journal of Geometric Methods in Modern Physics, 8(2011), no.1, 107-113.
There are 16 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Gözde özkan Tükel This is me

Ahmet Yücesan

Publication Date October 30, 2015
Published in Issue Year 2015

Cite

APA Tükel, G. ., & Yücesan, A. (2015). ELASTIC CURVES IN A TWO-DIMENSIONAL LIGHTLIKE CONE. International Electronic Journal of Geometry, 8(2), 1-8. https://doi.org/10.36890/iejg.592272
AMA Tükel G, Yücesan A. ELASTIC CURVES IN A TWO-DIMENSIONAL LIGHTLIKE CONE. Int. Electron. J. Geom. October 2015;8(2):1-8. doi:10.36890/iejg.592272
Chicago Tükel, Gözde özkan, and Ahmet Yücesan. “ELASTIC CURVES IN A TWO-DIMENSIONAL LIGHTLIKE CONE”. International Electronic Journal of Geometry 8, no. 2 (October 2015): 1-8. https://doi.org/10.36890/iejg.592272.
EndNote Tükel G, Yücesan A (October 1, 2015) ELASTIC CURVES IN A TWO-DIMENSIONAL LIGHTLIKE CONE. International Electronic Journal of Geometry 8 2 1–8.
IEEE G. . Tükel and A. Yücesan, “ELASTIC CURVES IN A TWO-DIMENSIONAL LIGHTLIKE CONE”, Int. Electron. J. Geom., vol. 8, no. 2, pp. 1–8, 2015, doi: 10.36890/iejg.592272.
ISNAD Tükel, Gözde özkan - Yücesan, Ahmet. “ELASTIC CURVES IN A TWO-DIMENSIONAL LIGHTLIKE CONE”. International Electronic Journal of Geometry 8/2 (October 2015), 1-8. https://doi.org/10.36890/iejg.592272.
JAMA Tükel G, Yücesan A. ELASTIC CURVES IN A TWO-DIMENSIONAL LIGHTLIKE CONE. Int. Electron. J. Geom. 2015;8:1–8.
MLA Tükel, Gözde özkan and Ahmet Yücesan. “ELASTIC CURVES IN A TWO-DIMENSIONAL LIGHTLIKE CONE”. International Electronic Journal of Geometry, vol. 8, no. 2, 2015, pp. 1-8, doi:10.36890/iejg.592272.
Vancouver Tükel G, Yücesan A. ELASTIC CURVES IN A TWO-DIMENSIONAL LIGHTLIKE CONE. Int. Electron. J. Geom. 2015;8(2):1-8.