Fronts of Whitney umbrella – a differential geometric approach via blowing up

Toshizumi Fukui and Masaru Hasegawa

Journal of Singularities
volume 4 (2012), 35-67

Received: 3 October 2011. Received in revised form: 9 January 2012.

DOI: 10.5427/jsing.2012.4c

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We investigate the differential geometric ingredients for Whitney umbrella, which is known as the only stable singularity of surface to 3-dimensional Euclidean space. We obtain several criteria of the singularity types of fronts of Whitney umbrella in terms of differential geometric language we discuss.


Whitney umbrella, Cross-cap, Singularities, Distance squared function, Blowing up, Front

Mathematical Subject Classification:

Primary 53A05; Secondary 58K20

Author(s) information:

Toshizumi Fukui Masaru Hasegawa
Department of Mathematics, Faculty of Science Department of Mathematics, Faculty of Science
Saitama University Saitama University
255 Shimo-Okubo 255 Shimo-Okubo
Sakura-ku, Saitama 338-8570, Japan Sakura-ku, Saitama 338-8570, Japan
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