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A Zeuthen Segre formula for even dimensional submanifolds of real projective space

  • J. W. Bruce (a1)
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In this paper we generalise results of Craveiro de Carvalho ([3]) in two ways. First we prove the following fact.

PROPOSITION 1. Given any smooth submanifold M of real projective spacen, for L in an open dense subset of the space of codimension 2 subspaces ofnwe have

(a) L meets M transversally and

(b) the pencil of hyperplanes through L have at worst Morse (A1) contact with M.

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Copyright
References
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1.Androtti, A. and Frankel, T., The Lefschetz hyperplane theorems in Global AnalysisPapers in Honour of K. Kodaira. (1969).
2.Bruce, J. W., Giblin, P. J. and Gibson, C. G., Caustics by reflection. Topology. To appear.
3.de Carvalho, F. J. Craveiro, Immersed surfaces and pencils of planes in 3-space. Glasgow Math. J. 22 (1981), 133136.
4.Mather, J., Generic projections. Annals of Maths., 98 (1973), 226245.
5.Milnor, J., Morse theory, Annals of Maths. Studies 51. (Princeton University Press, 1963).
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Glasgow Mathematical Journal
  • ISSN: 0017-0895
  • EISSN: 1469-509X
  • URL: /core/journals/glasgow-mathematical-journal
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