Abstract
We study the caustic, evolute, Minkowski symmetry set and parallels of a smooth and regular curve in the Minkowski plane.
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Arnol’d V.I.: Wave front evolution and equivariant Morse Lemma. Comm. Pure Appl. Math. 29, 557–582 (1976)
Arnol’d, V.I., Gusein-Zade, S.M., Varchenko, A.N.: Singularities of Differentiable Maps, vol. I. Birkhäuser (1986)
Bruce J.W.: Wavefronts and parallels in Euclidean space. Math. Proc. Camb. Phil. Soc. 93, 323–333 (1983)
Bruce J.W.: A note on first order differential equations of degree greater than one and wavefront evolution. Bull. Lond. Math. Soc. 16, 139–144 (1984)
Bruce J.W., Giblin P.J.: Curves and Singularities. Cambridge University Press, Cambridge (1984)
Dara L.: Singularités génériques des équations differentielles multiformes. Bol. Soc. Brasil Math. 6, 95–128 (1975)
Davydov, A.A.: Qualitative Control Theory. Translations of Mathematical Monographs 142. AMS, Providence RI (1994)
Giblin P.J., Brassett S.A.: Local symmetry of plane curves. Amer. Math. Mon. 92, 689–707 (1985)
Khesin B., Tabachnikov S.: Pseudo-Riemannian geodesics and billiards. Adv. Math. 221, 1364–1396 (2009)
O’Neill B.: Semi-Riemannian Geometry. With applications to relativity. Pure and Applied Mathematics. Academic Press, London (1983)
Öztekin H.B., Ergüt M.: Eigenvalue equations for Nonnull curve in Minkowski plane. Int. J. Open Probl. Compt. Math. 3, 467–480 (2010)
Siddiqi, K., Pizer, S.M. (eds.): Medial Representations Mathematics, Algorithms and Applications. Computational Imaging and Vision, vol. 37 (2008)
Tabachnikov S.: Parametrized plane curves, Minkowski caustics, Minkowski vertices and conservative line fields. Enseign. Math. 43, 3–26 (1997)
Tari F.: Caustics of surfaces in the Minkowski 3-space. Q. J. Math. 00, 1–21 (2010). doi:10.1093/qmath.laq030
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Amani Saloom was supported by a PhD grant from King Abdulaziz University.
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Saloom, A., Tari, F. Curves in the Minkowski plane and their contact with pseudo-circles. Geom Dedicata 159, 109–124 (2012). https://doi.org/10.1007/s10711-011-9649-1
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DOI: https://doi.org/10.1007/s10711-011-9649-1