Embeddings of nonorientable surfaces with totally reducible focal set
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Date
1994
Authors
Carter, Sheila
Journal Title
Journal ISSN
Volume Title
Publisher
Oxford Univ Press United Kingdom
Abstract
In an earlier paper [5] we introduced the idea of an immersion f:M W with totally reducible focal set.Such an immersion has the property that, for all peM, the focal set with base p is a union of hyperplanes in the normal plane to f(M) at .Trivially, this always holds if n=m+1 so we only consider n > m + 1.In [5] we showed that if M2 is a compact surface then for all n>4 there is a substantial immersion:A/2 R with totally reducible focal set. Further, if M2 is orientable or is a Klein bottle or a Klein bottle with handles then/:M2 W can be taken to be an embedding.Here we show that if M2 is a projective plane or a projective plane with handles then for all 5 there exists a substantial embedding f:M2 M with totally reducible focal set although,by arguments of M. Gromov and E. G. Rees,for n=4 such an embedding does not exist.
Description
Keywords
Mathematics, Orientation of surfaces, Unverified surfaces
Citation
Carter, S. ve Ezentaş, R. (1994). ''Embeddings of nonorientable surfaces with totally reducible focal set''. Glasgow Mathematical Journal, 36(1), 11-16.