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On generic hypersurfaces in ℝn

Published online by Cambridge University Press:  24 October 2008

J. W. Bruce
J. W. Bruce
Affiliation:
University College, Cork, Eire
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Extract

In this paper we consider certain questions concerning the differential geometry of generic hypersurfaces in ℝn. Our results prove, for example, that the curve of rib points of a generic surface in ℝ3 has transverse self-intersections.

In (4) Porteous discussed (amongst other things) the generic geometry of curves and surfaces in ℝ3. Subsequently Looijenga ((3) and see also (5)) gave a more precise definition of the term generic and showed that an open dense subset of smooth embeddings of manifolds in Euclidean space were indeed generic.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 90 , Issue 3 , November 1981 , pp. 389 - 394
Copyright
Copyright © Cambridge Philosophical Society 1981

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References

REFERENCES

(1)Bruce, J. W. Umbilics on generic surfaces. (To appear.)Google Scholar
(2)Golubitsky, M. and Guillemin, V.Stable mappings and their singularities, Graduate Texts in Mathematics, no. 14 (Springer Verlag, 1973).Google Scholar
(3)Looijenga, E. J. N. Structural stability of families of C ∞ functions. Thesis, University of Amsterdam (1974).Google Scholar
(4)Porteous, I. R.The normal singularities of a submanifold. Journal of Differential Geometry 5 (1971), 543–564.Google Scholar
(5)Wall, C. T. C.Geometric properties of generic differentiable manifolds. In Geometry and topology, vol. III, Springer Lecture Notes in Mathematics, no. 597 (1976).Google Scholar