Tohoku Mathematical Journal
2023
March
SECOND SERIES VOL. 75, NO. 1

Tohoku Math. J.
75 (2023), 131-141

Title SYMMETRIES OF CROSS CAPS

Author Atsufumi Honda, Kosuke Naokawa, Kentaro Saji, Masaaki Umehara and Kotaro Yamada

(Received April 21, 2021, revised November 8, 2021)
Abstract. It is well-known that cross caps on surfaces in the Euclidean 3-space can be expressed in Bruce-West's normal form, which is a special local coordinate system centered at the singular point. In this paper, we show a certain kind of uniqueness of such a coordinate system. In particular, the functions associated with this coordinate system produce new invariants on cross cap singular points. Using them, we characterize the possible symmetries on cross caps.

Mathematics Subject Classification. Primary 57R45; Secondary 53A05.
Key words and phrases. Singular point, cross cap, Whitney's umbrella.

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