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March 2021 Generic distance-squared mappings on plane curves
Shunsuke Ichiki
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Hiroshima Math. J. 51(1): 65-76 (March 2021). DOI: 10.32917/h2020010


A distance-squared function is one of the most significant functions in the application of singularity theory to differential geometry. Moreover, distance-squared mappings are naturally extended mappings of distance-squared functions, wherein each component is a distance-squared function. In this paper, compositions of a given plane curve and generic distance-squared mappings on the plane into the plane are investigated from the viewpoint of stability.

Funding Statement

The author was supported by JSPS KAKENHI Grant Numbers JP16J06911 and JP19J00650.


The author is most grateful to the anonymous reviewer for carefully reading the first manuscript of this paper and for giving invaluable suggestions. The author is grateful to Takashi Nishimura for his kind comments.


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Shunsuke Ichiki. "Generic distance-squared mappings on plane curves." Hiroshima Math. J. 51 (1) 65 - 76, March 2021.


Received: 6 February 2020; Revised: 8 June 2020; Published: March 2021
First available in Project Euclid: 19 April 2021

Digital Object Identifier: 10.32917/h2020010

Primary: 57R45
Secondary: 57R35

Keywords: curvature , distance-squared mapping , immersion with normal crossings , stability

Rights: Copyright © 2021 Hiroshima University, Mathematics Program


Vol.51 • No. 1 • 2021
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