Topological classification of the tangent developables of space curves

Journal of the London Mathematical Society

Volumn 62, Issue 2, 2000, Pages 583-598

  Ishikawa, Goo ^a  

^a HOKKAIDO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034288586     PISSN: 00246107     EISSN: None     Source Type: Journal    
DOI: 10.1112/S0024610700001095     Document Type: Article

References (27)

1. V. I. ARNOLD, Singularities of caustics and wave fronts (Kluwer, Dordrecht, 1990).
2. V. I. ARNOLD, Topological invariants of plane curves and caustics, University Lecture Series 5 (American Mathematical Society, Providence, RI, 1994).
3. J. J. NUÑO BALLESTEROS, 'On the number of the triple points of the tangent developable', Geom. Dedicata 47 (1993) 241-254.
4. J. W. BRUCE, 'On contact of hypersurfaces', Bull. London Math. Soc. 13 (1981) 51-54.
5. J. W. BRUCE and P. J. GIBLIN, Curves and singularities, 2nd edn (Cambridge University Press, 1992).
6. A. CAYLEY, 'On the developable surfaces which arise from two surfaces of second order', Cambridge Dublin Math. J. 2 (1850) 46-57; The collected mathematical papers - Vol. I (Cambridge University Press, 1963) 486-495.
7. A. CAYLEY, 'On the developable surfaces which arise from two surfaces of second order', Cambridge Dublin Math. J. 2 (1850) 46-57; The collected mathematical papers - Vol. I (Cambridge University Press, 1963) 486-495.
8. J. P. CLEAVE, 'The form of the tangent developable at points of zero torsion on space curves', Math. Proc. Cambridge Philos. Soc. 88 (1980) 403-407.
9. T. GAFFNEY and A. DU PLESSIS, 'More on the determinacy of smooth map-germs', Invent. Math. 66 (1982) 137-163.
10. C. G. GIBSON, K. WIRTHMÜLLER, A. A. DU PLESSIS and E. J. N. LOOIJENGA, Topological stability of smooth mappings, Lecture Notes in Mathematics 552 (Springer, 1976).
11. A. B. GIVENTAL, 'Lagrangian imbeddings of surfaces and unfolded Whitney umbrella', Funksional Anal. i Prilozhen. 20 (1986) 35-41.
12. G. ISHIKAWA, 'Determinacy of envelope of the osculating hyperplanes to a curve', Bull. London Math. Soc. 25 (1993) 603-610.
13. G. ISHIKAWA, 'Parametrized Legendre and Lagrange varieties', Kodai Math. J. 17 (1994) 442-451.
14. G. ISHIKAWA, 'Developable of a curve and its determinacy relatively to the osculation-type', Quart. J. Math. 46 (1995) 437-451.
15. S. JANECZKO and M. ROBERTS, 'Classifications of symmetric caustics I: symplectic equivalence', Singularity theory and its application II, Lecture Notes in Mathematics 1463 (ed. M. Roberts and I. Stewart, Springer, 1991), 193-219.
16. A. G. KHOVANSKIǏ, Fewnomials, Translations of Mathematical Monographs 88 (American Mathematical Society, Providence, RI, 1991).
17. 1-equivalence of functions near isolated critical points', Annals of Mathematics Studies 69 (Princeton University Press, 1972) 199-218 (Symposium in Infinite Dimensional Topology, Baton Rouge, 1967).
18. 0 sufficiency of functions near isolated critical points', Topology 8 (1969) 167-171.
19. D. MOND, 'On the tangent developable of a space curve', Math. Proc. Cambridge Philos. Soc. 91 (1982) 351-355.
20. D. MOND, 'Singularities of the tangent developable surface of a space curve', Quart. J. Math. Oxford 40 (1989) 79-91.
21. I. R. PORTEOUS, Geometric differentiation, for the intelligence of curves and surfaces (Cambridge University Press, 1994).
22. O. P. SHCHERBAK, 'Projectively dual space curves and Legendre singularities', Trudy Tbiliss. Univ. 232-233 (1982) 280-336; Sel. Math. Sov. 5 (1986) 391-421.
23. O. P. SHCHERBAK, 'Projectively dual space curves and Legendre singularities', Trudy Tbiliss. Univ. 232-233 (1982) 280-336; Sel. Math. Sov. 5 (1986) 391-421.
24. O. P. SHCHERBAK, 'Wavefront and reflection groups', Russian Math. Surveys 43 (1988) 149-194.
25. J. J. STOKER, Differential geometry, Pure and Applied Mathematics 20 (John Wiley, New York, 1969).
26. C. T. C. WALL, 'Finite determinacy of smooth map-germs', Bull. London Math. Soc. 13 (1981) 481-539.
27. C. T. C. WALL, 'Duality of singular plane curves', J. London Math. Soc. (2) 50 (1994) 265-275.