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The Total Absolute Curvature of Nonclosed Curves in S2

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Abstract

The total absolute curvature of nonclosed curves in S2 is studied. We look at the set of curves with fixed endpoints and end-directions and see how the infimum of the total absolute curvature in this set depends on the endpoints and the end-directions. We consider both the case when the length of curves is fixed and the case when the length is free, and see the difference of results between them.

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Authors and Affiliations

  1. Faculty of Industrial Science and Technology, Tokyo University of Science, Oshamambe, Hokkaido, 049-3514, Japan

    Kazuyuki Enomoto

  2. Faculty of Education, Kumamoto University Kumamoto, Kumamoto, 860-8555, Japan

    Jin-ichi Itoh

Authors
  1. Kazuyuki Enomoto
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  2. Jin-ichi Itoh
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Correspondence to Kazuyuki Enomoto.

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Enomoto, K., Itoh, Ji. The Total Absolute Curvature of Nonclosed Curves in S2 . Results. Math. 45, 21–34 (2004). https://doi.org/10.1007/BF03322994

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  • DOI: https://doi.org/10.1007/BF03322994

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