open access

https://doi.org/10.14943/84215

https://hdl.handle.net/2115/69875

Legendre curves in the unit spherical bundle and evolutes

英語

2015-06-19

Department of Mathematics, Hokkaido University

Hokkaido University Preprint Series in Mathematics

1071

1-19

In order to consider singular curves in the unit sphere, we consider Legendre curves in the unit spherical bundle. By using a moving frame, we de ne the curvature of Legendre curves in the unit spherical bundle. As applications, we give a relationship among Legendre curves in the unit spherical bundle, Legendre curves in the unit tangent bundle and framed curves in the Euclidean space, respectively. Moreover, we de ne not only an evolute of a front, but also an evolute of a frontal in the unit sphere under certain conditions. Since the evolute of a front is also a front, we can take evolute again. On the other hand, the evolute of a frontal if exists, is also a frontal. We give an existence and uniqueness conditions of the evolute of a frontal.

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