Singularities of ruled surfaces in ℝ3

Mathematical Proceedings of the Cambridge Philosophical Society

Volumn 130, Issue 1, 2001, Pages 1-11

  Izumiya, Shyuichi ^a   Takeuchi, Nobuko ^b  

^a HOKKAIDO UNIVERSITY   (Japan)

^b TOKYO GAKUGEI UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 23044521735     PISSN: 03050041     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0305004100004643     Document Type: Article

References (19)

1. V. I. ARNOL'D, S. M. GUSEIN-ZADE and A. N. VARCHENKO. Singularities of differentiable maps, vol. I (Birkhäuser, 1986).
2. T. BANCHOFF. Front cover of Notices of of A.M.S. (http://www.geom.umn.edu/locate/tfb/art/), vol. 44, no. 3 (1997).
3. J. P. CLEAVE. The form of the tangent developable at points of zero torsion on space curves. Math. Proc. Camb. Phil. 88 (1980), 403-407.
4. C. G. GIBSON, K. WIRTHMÜLLER, A. A. DU PLESSIS and E. J. N. LOOIJENGA. Topological stability of Smooth Mappings. Lecture Notes in Math. 552 (Springer, 1970).
5. M. GOLUBITSKY and V. GUILLEMIN. Stable mappings and their singularities, GTM 14 (Springer, 1973).
6. A. GRAY. Modern differential geometry of curves and surfaces (CRC Press, 1993).
7. J. HOSCHEK and H. POTTMAN. Interpolation and approximation with developable B-spline surfaces, in Mathematical Methods for curves and surfaces (ed. M. Dæhlen, T. Lyche and L. L. Schumacker), pp. 255-264 (Vanderbilt Univ. Press, 1995).
8. G. ISHIKAWA. Determinacy of envelope of the osculating hyperplanes to a curve. Bull. London Math. Soc. 25 (1993), 787-798.
9. G. ISHIKAWA. Developable of a curve and determinacy relative to osculation-type. Quart. J. Math. Oxford 46 (1995), 437-451.
10. S. IZUMIYA and T. SANO. Generic affine differential geometry of space curves. Proceedings of the Royal Society of Edinburgh, vol. 128A (1998), 301-314.
11. S. IZUMIYA, H. KATSUMI and T. YAMASAKI. The rectifying developable and the Darbopux indicatrix of a space curve. Banach Center Publications, Caustics '98, vol. 50 (1999), 137-149.
12. S. IZUMIYA, D.-H. PEI and T. SANO. The lightcone Gauss map and the lightcone developable of a spacelike curve in Minkowski 3-space, Glasgow Math. J. 42 (2000), 75-89.
13. J. MARTINET. Singularities of smooth functions and maps, London Math. Soc. Lecture Note Series, vol. 58 (Cambridge University Press, 1982).
14. D. MOND. Singularities of the tangent developable surface of a space curve. Quart. J. Math. Oxford 40 (1989), 79-91.
15. I. PORTEOUS. The normal singularities of submanifold. J. Diff. Geom. 5 (1971), 543-564.
16. T. SASAKI. Projective differential geometry and linear homogeneous differential equations. Rokko Lectures in Mathematics, Kobe University, vol. 5 (1999).
17. O. P. SCHERBAK. Projectively dual space curve and Legendre singularities. Sel. Math. Sov. 5 (1986), 391-421.
18. M. SCHNEIDER. Interpolation with developable strip-surfaces consisting of cylinders and cones, in mathematical methods for curves and surfaces II, (ed. M. Dæhlen, T. Lyche and L. L. Schumacker), pp. 437-444 (Vanderbilt University Press, 1998).
19. H. WHITNEY. The singularities of a smooth n-manifold in (2n - 1)-space. Annals of Math. 45 (1944), 247-293.