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Keywords:
geometry; curve; surface
References:
[1] Verstraelen, L.: The geometry of eye and brain. Soochow Journal of Mathematics 30 (2004) (volume in honour of Professor Bang-Yen Chen), 367–376. MR 2093862 | Zbl 1131.92303
[2] Coolidge, J. L.: A history of geometrical methods. Dover Publ., London (1963). MR 0160143 | Zbl 0113.00103
[3] Bronowski, J.: The ascent of man. Litte, Brown & Co, Boston 1973.
[4] Lejeune, A.: Euclide et Ptolémée, deux stades de l’optique géométrique grecque. Université de Louvain, Bureau du “Recueil” (1948). MR 0028212 | Zbl 0039.24102
[5] Montel, P.: Encyclopédie française, Tome 1. Larousse, Paris 1937.
[6] Dillen, F., Verstraelen, L.: Handbook of differential geometry. North-Holland, Amsterdam, Vol. 1 (2000) and Vol. 2 (2005). MR 1736851 | Zbl 1069.00010
[7] Chern, S. S., Chen, W. H., Laser, K. S.: Lectures on differential geometry. World Scientific, Singapore 1999. MR 1735502
[8] Kühnel, W.: Differential geometry: curves-surfaces-manifolds. AMS-Student Math. Library, vol. 16 (2002). MR 1882174 | Zbl 1009.53002
[9] Penrose, R.: The geometry of the universe. In Mathematics Today (ed. Steen, L. A.), Vintage Books, New York 1980. MR 0599181
[10] Penrose, R.: The emperor’s new mind, concerning computers, minds and the laws of physics. Oxford University Press, Oxford 1989. MR 1048125
[11] Browder, F. E., Mac Lane, S.: The relevance of mathematics. In Mathematics Today (ed. Steen, L. A.), Vintage Books, New York 1980.
[12] Hilbert, D.: Mathematical problems (1900 – Paris – Lecture). AMS-Proceedings of Symposia in Pure Mathematics, Vol. 28 (1976).
[13] d’Arcy Thompson, W.: On growth and form. Cambridge University Press, Cambridge 1917. MR 0128562
[14] Lamé, G.: Examen des différentes méthodes employées pour résoudre les problèmes de géométrie. Hermann, Paris 1818.
[15] Thompson, A. C.: Minkowski geometry. Encyclopedia of mathematics and its applications, Vol. 63, Cambridge University Press, Cambridge 1996. MR 1406315 | Zbl 0868.52001
[16] Chen, B.-Y.: What can we do with Nash’s embedding theorem?. Soochow Journal of Mathematics 30 (2004), 303–338. MR 2093858 | Zbl 1077.53044
[17] Chen, B.-Y.: Riemannian submanifolds. In [6, Vol. 1]. Zbl 1079.53077
[18] Hildebrandt, S., Tromba, A.: Panoptimum. Spektrum, Heidelberg 1986. MR 1040828
[19] Willmore, T. J.: A survey on Willmore immersions. In Geometry and Topology of submanifolds, Vol. IV, (eds. Dillen, F., Verstraelen, L.), World Scientific, Singapore 1992. MR 1185712 | Zbl 0841.53051
[20] Chen, B.-Y.: Total mean curvature and submanifolds of finite type. World Scientific, Singapore 1984. MR 0749575 | Zbl 0537.53049
[21] Barros, M.: The conformal total tension variational problem in Kaluza-Klein supergravity. Nuclear Physics B 535 (1998), 531–551. DOI 10.1016/S0550-3213(98)00601-4 | MR 1666496 | Zbl 1041.83512
[22] Barros, M.: Willmore-Chen branes and Hopf T-duality. Class. Quantum Grav. 17 (2000), 1979–1988. DOI 10.1088/0264-9381/17/9/308 | MR 1764006 | Zbl 0967.83031
[23] Gielis, J., Haesen, S., Verstraelen, L.: Universal natural shapes; from the supereggs of Piet Hein to the cosmic egg of Georges Lemaître. Kragujevac Journal of Mathematics 28 (2005), 57–68. MR 2211243
[24] Gielis, J.: A generic transformation that unifies a large number of natural and abstract shapes. American Journal of Botamy 90 (2003), 333–338. DOI 10.3732/ajb.90.3.333
[25] Gielis, J.: Inventing the circle. Geniaal Press, Antwerpen (2003).
[26] Gielis, J., Gerats, T.: A botanical perspective on plant shape modeling. Proc. International Conference on Computing, Communications and Control Technologies, Vol. VI (2004), 265–272.
[27] Gielis, J.: Wiskundige supervormen bij bamboes. Newsletter Belgian Bamboo Society 13 (1996), 20–26.
[28] Gielis, J., Beirinckx, B., Bastiaens, E.: Superquadrics with rational and irrational symmetries. Proc. 8th ACM symposium on Solid Modeling and Applications (2003), 262–265.
[29] Gielis, J.: Variational superformula curves for 2D- and 3D graphic arts. Proc. World Multi-Conference on Systemics, Cybernetics and Informatics, Vol. V: Computer Science and Engineering (2004), 119–124.
[30] Haesen, S., Sebeković, A., Verstraelen, L.: Relations between intrinsic and extrinsic curvatures. Kragujevac J. Math. 25 (2003), 139–145. MR 2120586 | Zbl 1274.53024
[31] Dillen, F., Haesen, S., Petrović-Torgasev, M., Verstraelen, L.: An inequality between intrinsic and extrinsic scalar curvature invariants for codimension 2 embeddings. J. Geom. Phys. 52 (2004), 101–112. DOI 10.1016/j.geomphys.2004.02.003 | MR 2088970 | Zbl 1083.53062
[32] Haesen, S., Verstraelen, L.: Ideally embedded space-times. J. Math. Phys. 45 (2004), 1497–1510. DOI 10.1063/1.1668333 | MR 2043839 | Zbl 1068.53053
[33] Lemaître, G.: Un univers homogène de masse constante et de rayon croissant, rendant compte de la vitesse radiale des nébuleuses extra-galactique. Annales Soc. Sc. Bruxelles 47 (1927), 49–59.
[34] O’Neill, B.: Semi-Riemannian geometry, with applications to relativity. Acad. Press, New York 1983. MR 0719023
[35] Helmholtz, H. von: Ueber die Tatsachen welche der Geometrie zu Grunde liegen. In Abhandlungen zur Philosophie und Geometrie, Junghaus, Cuxhausen 1987.
[36] Riemann, B.: Ueber die Hypothesen welche der Geometrie zu Grunde liegen. In Gaussche Flächentheorie, Riemannsche Räume und Minkowski-Welt, Teubner, Leipzig 1984.
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