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Title: Embeddings of nonorientable surfaces with totally reducible focal set
Authors: Carter, Sheila
Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Bölümü.
Ezentaş, Rıdvan
Keywords: Mathematics
Orientation of surfaces
Unverified surfaces
Issue Date: 1994
Publisher: Oxford Univ Press United Kingdom
Citation: Carter, S. ve Ezentaş, R. (1994). ''Embeddings of nonorientable surfaces with totally reducible focal set''. Glasgow Mathematical Journal, 36(1), 11-16.
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.
ISSN: 0017-0895
Appears in Collections:Scopus
Web of Science

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