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FAMILIES OF SURFACES IN ℝ4

Published online by Cambridge University Press:  05 February 2002

J. W. Bruce  and
F. Tari
J. W. Bruce
Affiliation:
Department of Pure Mathematics, The University of Liverpool, PO Box 147, Liverpool L69 3BX, UK (jwbruce@liv.ac.uk)
F. Tari
Affiliation:
Universidade de São Paulo, Instituto de Matemática e de Computação, Caixa Postal 668, CEP 13560-970, São Carlos (SP), Brasil (tari@icmsc.sc.usp.br)
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Abstract

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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

Keywords

surfacessingularitiesparabolic setasymptotic curvesbifurcations
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 45 , Issue 1 , February 2002 , pp. 181 - 203
Copyright
Copyright © Edinburgh Mathematical Society 2002