By P. Baird, J. Eells (auth.), E. Looijenga, D. Siersma, F. Takens (eds.)
Read or Download Geometry Symposium Utrecht 1980: Proceedings of a Symposium Held at the University of Utrecht, The Netherlands, August 27–29, 1980 PDF
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Extra resources for Geometry Symposium Utrecht 1980: Proceedings of a Symposium Held at the University of Utrecht, The Netherlands, August 27–29, 1980
Sample text
L• XI/2 / if the vec- X . This compression / 1 00 yl/2 i/ >1 v yO 31 We have then modified in a half space, the original general pair say the right half-space line. V = i} is parallel the value of the polygon Y , again rotating to X,Y H(X,Y) V slightly if necessary so that V . We end up with a general pair of polygons V . Since these two lines are distinct, ~o(~ ~ now lies remains unchanged. V ~ 0} ~oX and one of the cri- ~V-t~ . We get a same side double support if we take -t ~voX a n d o n e o f t h e ~o(~ -to V Y) m i n i m a o f minima of !
Mension fer [I] still greater difficulties, However, we note that for p < n/4 , there is a generalization . Under the hypotheses of Thomas's of that theorem, remaining equations needed for an embedding, and the problem is again reduced to an this theorem. 4 and codi- theorem due to Allendoer- proof of Allendoerfer's the question of the "genericity" which may be viewed as a codimension-two n ~ 4 even in the Gauss equations again imply the algebraic one. 4) an alternative theorem. Finally, we consider are stated for the of the hypotheses hypersurface minimal submanifold form is non-singular, of in ~m for m> in 5 , LR2m .
X(u) - Y(v) is a non- and simultaneously, in . For immersions in general position there will be a finite number of double tangencies W -iX(u)_Y(v) I . This integer X . so that the secant vector zero vector lying in the tangent space to the tangent space to ~4 ,[2]) into ZwIOX Zw•176 will have a Whitney pinch point at (u,v) and if we sight down the unit vector ~3 (WI) , this projection will be general will have a Whitney pinch point at v . X(u) : M2 ~ ~4 > O X for all nearly Y' : N2 + ~4 where = ~x,(U,V) and ~y,(V,W) z ~x,y(U,V) = in M2 we compress .