Scientific and Educational Reports of the Faculty

of Science and Technology, Kochi University

Vol. 5 (2022), No. 8

### On the existence of a rotational closed chain

Kazushi Komatsu，Jun Yagi

Faculty of Science and Technology, Kochi University ； Akebono-cho 2-5-1, Kochi 780-8520, Japan

要旨

The set of closed chains is called the configuration space of the closed chains. Let M_{n}^{n} (θ) be the configuration space of equilateral and equiangular closed chains
with the bond angle θ and n-vertices, and M_{n}^{n-2} (θ) the configuration space of equilateral closed chains with n-vertices whose n−2 bond angles are the same θ except for successive two angles. In this paper, we study the condition of n for which M_{n}^{n}(π/ 2) or M_{n}^{n-2} (cos^{-1} (− 1/ 3)) has a rotational closed chain. This results give a geometrical
approach for the study of the topology of M_{n}^{n} (π/ 2) or M_{n}^{n-2} (cos^{-1} (− 1/ 3)).

Received: March 12, 2022

Reviewed by anonymous referee(s), and accepted: May 19, 2022

Published: June 22, 2022

発行者：高知大学理工学部 〒780-8520 高知県高知市曙町二丁目5-1

Faculty of Science and Technology, Kochi University, Kochi, 780-8520 Japan

問い合わせ先（E-mail）：serfst●kochi-u.ac.jp （送信の際は"●"を半角"@"に変更して送信してください）

高知大学理工学部

高知大学