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.
Citation
Atsufumi Honda. Kosuke Naokawa. Kentaro Saji. Masaaki Umehara. Kotaro Yamada. "Symmetries of cross caps." Tohoku Math. J. (2) 75 (1) 131 - 141, 2023. https://doi.org/10.2748/tmj.20211203
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