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DUALITY AND CONTACT OF HYPERSURFACES IN $\mathbb{R}^4$ WITH HYPERPLANES AND LINES

Published online by Cambridge University Press:  10 December 2003

A. C. Nabarro
A. C. Nabarro
Affiliation:
Departamento de Matemática, Universidade Estadual de Maringá, Av. Colombo 5790, Campus Universitário, CEP 87020-900, Maringá, PR, Brazil (acnabarro@uem.br)
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Abstract

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Given an embedded hypersurface $M$ in $\mathbb{R}^4$ we consider families of projections $H$ of $M$ to lines and families of projections $P$ of $M$ to 3-spaces. We characterize generically the singularities of these projections. We also show that there is a duality relation between some strata of the bifurcation sets of $H$ and $P$, and deduce geometric properties about these sets.

AMS 2000 Mathematics subject classification: Primary 58K05. Secondary 58K40

Keywords

singularitiesgeneric geometryduality
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 46 , Issue 3 , October 2003 , pp. 637 - 648
Copyright
Copyright © Edinburgh Mathematical Society 2003