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asymptotic curves

Proceedings of the Edinburgh Mathematical Society (1)

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FAMILIES OF SURFACES IN ℝ4
J. W. Bruce, F. Tari
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 45 / Issue 1 / February 2002

Published online by Cambridge University Press:

05 February 2002, pp. 181-203
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We study the geometry of surfaces in $\mathbb{R}^4$ associated to contact with hyperplanes. We list all possible transitions that occur on the parabolic and so-called $A_3$-set, and analyse the configurations of the asymptotic curves and their bifurcations in generic one-parameter families.
AMS 2000 Mathematics subject classification: Primary 58C27. Secondary 53A05