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

Published online by Cambridge University Press:  18 May 2009

J. W. Bruce
J. W. Bruce
Affiliation:
University College, Cork, Eire
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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 space ℙn, for L in an open dense subset of the space of codimension 2 subspaces of ℙnwe have

(a) L meets M transversally and

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

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 24 , Issue 1 , January 1983 , pp. 97 - 99
Copyright
Copyright © Glasgow Mathematical Journal Trust 1983

References

REFERENCES

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5.Milnor, J., Morse theory, Annals of Maths. Studies 51. (Princeton University Press, 1963).Google Scholar