ELASTIC CURVES IN A TWO-DIMENSIONAL LIGHTLIKE CONE

Year 2015, Volume: 8 Issue: 2, 1 - 8, 30.10.2015

Gözde özkan Tükel Ahmet Yücesan

https://doi.org/10.36890/iejg.592272

Cited By: 3

Abstract

Keywords

Elastic curves, Euler-Lagrange equations, Lightlike cone

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.