Given any finite subset X of the sphere S, n ≥ 2, which includes no pairs of antipodal points, we explicitly construct smoothly immersed closed orientable hypersurfaces in Euclidean space R whose Gauss map misses X. In particular, this answers a question of M. Gromov.

As an initial step to a broader study of the disorienting effects of cold water immersions on top class competitive canoeists a survey was made of the incidence of hazardous immersions amongst a majority sample of the better canoeists in the country. Virtually the entire entry to one of the most important national competitive meets was canvassed. A total of 288 canoeists in the 1st and 2nd divi...

Criminal profiling, referred to as offender profiling, psychological profiling or criminal personality profiling, is the derivation of inferences about a criminal from aspects of the crime (s) that he or she has committed. Available information from a crime and crime scene theoretically should point to a psychological portrait of the unknown perpetrator inferring such things as the offender’s m...

M. Hirsch and independently H. Glover have shown that a closed ¿-connected smooth «-manifold M embeds in R2n~> if Mo immerses in A*""*-1, jè2k and 2/gra — 3. Here Mo denotes M minus the interior of a smooth disk. In this note we prove the converse and show also that the isotopy classes of embeddings of M in i?a"-»' are in one-one correspondence with the regular homotopy classes of immersions of...

The universal order 1 invariant fU of immersions of a closed orientable surface into R3, whose existence has been established in [T. Nowik, Order one invariants of immersions of surfaces into 3-space, Math. Ann. 328 (2004) 261–283], is the direct sum

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In the preceding article [T], we have constructed several examples of slant immersions into complex Euclidean spaces. The purpose of this article is to construct some additional examples to get slant and full immersions, in the sense of slantedness, into complex Euclidean spaces with arbitrary dimension, codimension, and positive slant angle.

1. Let M and M' denote complete riemannian manifolds of dimension n and m respectively, and suppose that M is compact and oriented. For simplicity we assume that both manifolds and their metrics are smooth (i.e. of class C). In terms of local co-ordinates (x, x, ...,x") on M and local co-ordinates (y,y, •••,/") on M', the riemannian metrics are written ds = gtJ dx l dx, ds' = g'aP dy* dy * wher...