Singularities of line congruences

Royal Society of Edinburgh - Proceedings A

Volumn 133, Issue 6, 2003, Pages 1341-1359

  Izumiya, Shyuichi ^a   Saji, Kentaro ^b   Takeuchi, Nobuko ^c  

^a HOKKAIDO UNIVERSITY   (Japan)

^b HIROSHIMA UNIVERSITY   (Japan)

^c TOKYO GAKUGEI UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 1642491924     PISSN: 03082105     EISSN: None     Source Type: Journal    
DOI: 10.1017/s0308210500002973     Document Type: Article

References (20)

1. V. I. Arnol'd, S. M. Gusein-Zade and A. N. Varchenko. Singularities of differentiable maps, vol. I (Birkhäuser, 1986)
2. A. V. Bäcklund. Om ytor med konstant negativ krökning, vol. 19 (Lunds University Arsskrift, 1883). (Transl. Concerning surfaces with constant negative curvature (Lancaster, PA: New Erar Printing, 1905).)
3. A. V. Bäcklund. Om ytor med konstant negativ krökning, vol. 19 (Lunds University Arsskrift, 1883). (Transl. Concerning surfaces with constant negative curvature (Lancaster, PA: New Erar Printing, 1905).)
4. L. Bianchi. Lezionidi geometria differenziale. In Terza edizione internamente rifatta (Bologna: Nicola Zanichelli, 1927).
5. T. Cecil. Focal points and support functions in affine differential geometry. Geom. Dedicata 50 (1994), 291-300.
6. L. P. Eisenhart, A treatise on the differential geometry of curves and surfaces (Oxford: Ginn and Company, 1909).
7. C. G. Gibson. Singular points of smooth mappings. Research Notes in Mathematics, vol. 25 (Boston, MA: Pitman, 1979).
8. C. G. Gibson, K. Wirthmüller, A. A. du Plessis and E. J. N. Looijenga. Topological stability of smooth mappings Lecture Notes in Mathematics, vol. 552 (Springer, 1970).
9. M. Golubitsky and V. Guillemin. Stable mappings and their singularities. Graduate Text in Mathematics, vol. 14 (Springer, 1973).
10. S. Izumiya and T. Sano. Generic affine differential geometry of plane curves. Proc. Edinb. Math. Soc. 41 (1998), 315-324.
11. 3. Math. Proc. Camb. Phil. Soc. 130 (2001), 1-11.
12. ∞-functions. PhD thesis, Universiteit van Amsterdam (1974).
13. J. Martinet. Singularities of smooth functions and maps. London Mathematics Society Lecture Note Series, vol. 58 (Cambridge University Press, 1982).
14. K. Nomizu and T. Sasaki. Affine differential geometry. Geometry of affine immersions. Cambridge Tracts in Mathematics, vol. 111 (Cambridge University Press, 1994).
15. I. Porteous. The normal singularities of a submanifold. J. Diff. Geom. 5 (1971), 543-564.
16. H. Pottman and J. Wallner. Computational line geometry (Springer, 2001).
17. K. Saji. Singularities of non-degenerate 2-ruled hypersurfaces in 4-space. Hiroshima Math. J. 32 (2002), 309-323.
18. T. Sasaki. Projective differential geometry and linear homogeneous differential equations. Rokko Lectures in Mathematics, vol. 5 (Kobe University, 1999).
19. M. D. Shepherd. Line congruences as surfaces in the space of lines. Diff. Geom. Applic. 10 (1999), 1-26.
20. C.-L. Terng and K. Uhlenbeck. Geometry of solitons. Not. Am. Math. Soc. 47 (2000), 17-25.