The normal singularities of a submanifold

Journal of Differential Geometry

Volumn 5, Issue 3-4, 1971, Pages 543-564

  Porteous, I R ^a  

^a UNIVERSITY OF LIVERPOOL   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84972503925     PISSN: 0022040X     EISSN: 1945743X     Source Type: Journal    
DOI: 10.4310/jdg/1214430015     Document Type: Article

References (30)

1. J. M. Boardman, Singularities of differentiable maps, Inst. Hautes Études Sci. Publ. Math. No. 33 (1967) 21-57.
2. A. Cayley, On differential equations and umbilici, Philos. Mag. 26 (1863) 373-379, 441-452 (Collected Works, Vol. V, paper 330).
3. A. Cayley, Note on Mr. Frost’s paper on the direction of lines of curvature in the neighbourhood of an umbilicus, Quart. J. Math. 10 (1870) 111-113 (Collected Works Vol. VII, paper 460).
4. A. Cayley, On the centro-surface of an ellipsoid, Trans. Cambridge Philos. Soc. 12 (1873) 319-365 (Collected Works Vol. VIII, paper 520).
5. G. Darboux, Leçons sur la théorie générales des surfaces, Vol. 4, Gauthier-Villars, Paris, 1896.
6. E. B. Elliott, An introduction to the algebra of quantics, Clarendon, Oxford, 1895.
7. E. A. Feldman, The geometry of immersions. II, Bull. Amer. Math. Soc. 70 (1964) 600-607.
8. E. A. Feldman, On parabolic and umbilic points of immersed hypersurfaces, Trans. Amer. Math. Soc. 127 (1967) 1-28.
9. P. Frost, On the directions of lines of curvature in the neighbourhood of an umbilicus, Quart. J. Math. 10 (1870) 78-86 and Plate 1 facing p. 96.
10. A. Gullstrand, Allgemeine Theorie der monochromatischen Aberrationen und ihre nächsten Ergebnisse für die Ophthalmologie, Nova Acta Regiae Soc. Sci. Ups. Ser. III (1900).
11. A. Gullstrand, Zur Kenntniss der Kreispunkte, Acta Math. 29 (1905) 59-100.
12. H. Hamburger, Beweis einer Caratheodoryschen Vermutung. I, Ann. of Math. (2) 41 (1940) 63-86; II, III, Acta Math. 73 (1941) 175-228, 229-332.
13. P. Hartman & A. Wintner, On the singularities in nets of curves defined by differential equations, Amer. J. Math. 75 (1953) 277-297.
14. K. Kommerell, Riemannschen Flächen im ebenen Raum von vier Dimensionen, Math. Ann. 60 (1905) 548-596.
15. T. C. Kuo, On C°-sufficiency of jets of potential functions, Topology 8 (1969) 167-171.
16. J. A. Little, On singularities of submanifolds of higher dimensional Euclidean spaces, Ann. Mat. Pura Appl. (IV) 83 (1969) 261-336.
17. n, Rec. Math. (Mat. Sbornik) N.S. 42 (1935) 81-100.
18. E. Picard, Traité d’analyse. Ill, Gauthier-Villars, Paris, 1896, 225-227.
19. I. R. Porteous, Simple singularities of maps, Columbia Universtiy notes, 1962; reprinted with slight revision in Proc. Liverpool Singularities Sympos. I, Lecture Notes in Math. Vol. 192, Springer, Berlin, 1971, 286-307.
20. I. R. Porteous, Topological geometry, Van Nostrand Reinhold, London, 1969.
21. I. R. Porteous, Geometric differentiation-a Thomist view of differential geometry, Proc. Liverpool Singularities Sympos. II, Lecture Notes in Math. Springer, Berlin, 1971.
22. 4, Volzh. Mat. Sb. Vyp. 3 (1965) 296-311 (Russian).
23. 4, Izv. Vyssh. Učhebn. Zaved. Mat. 6 (55) (1966) 137-143 (Russian).
24. S. A. Robertson, Toroidal maps, Sympos. seminar on singularities of smooth manifolds and maps (Liverpool), 1969-70.
25. J. A. Schouten & D. J. Struik, Einführing in die neueren Methoden der differential Geometrie, Vol. 2, Groningen-Batavia, 1938.
26. R. Thom, Sur la théorie des enveloppes, J. Math. Pures Appl. 41 (1962) 177-192.
27. R. Thom, Stabilité structurelle et morphogénèse, Benjamin, New York, to appear.
28. C. J. Titus, A proof of the Caratheodory conjecture concerning umbilic points, to appear.
29. I. A. Todd, Projective and analytical geometry, Pitman, London, 1947.
30. Y. C. Wong, A new curvature theory for surfaces in a Euclidean 4-space, Comment Math. Helv. 26 (1952) 152-170.