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SINGULARITIES OF HOROSPHERICAL HYPERSURFACES OF CURVES IN HYPERBOLIC 4-SPACE

Published online by Cambridge University Press:  22 September 2011

DONGHE PEI
DONGHE PEI*
Affiliation:
School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, PR China (email: peidh340@nenu.edu.cn)
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Abstract

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We consider the contact between curves and hyperhorospheres in hyperbolic 4-space as an application of the theory of singularities of functions. We define the osculating hyperhorosphere and the horospherical hypersurface of the curve whose singular points correspond to the locus of polar vectors of osculating hyperhorospheres of the curve. One of the main results is a generic classification of singularities of horospherical hypersurfaces of curves.

Keywords

hyperbolic spacehyperhorospherehorospherical height functionhorospherical hypersurface
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 91 , Issue 1 , August 2011 , pp. 89 - 101
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

References

[1]Arnol’d, V. I., Gusein-Zade, S. M. and Varchenko, A. N., Singularities of Differentiable Maps, Vol. I (Birkhäuser, Basel, 1986).Google Scholar
[2]Izumiya, S., Pei, D.-H. and Sano, T., ‘Singularities of hyperbolic Gauss maps’, Proc. Lond. Math. Soc. 86 (2003), 485–512.CrossRefGoogle Scholar
[3]Izumiya, S., Pei, D.-H. and Sano, T., ‘Horospherical surfaces of curves in hyperbolic space’, Publ. Math. Debrecen 64 (2004), 1–13.CrossRefGoogle Scholar
[4]Montaldi, J. A., ‘On generic composites of maps’, Bull. Lond. Math. Soc. 23 (1991), 81–85.CrossRefGoogle Scholar
[5]Wassermann, G., ‘Stability of caustics’, Math. Ann. 210 (1975), 43–50.CrossRefGoogle Scholar