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Invariants of non-developable ruled surfaces in Euclidean 3-space

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Abstract

In this paper, using the classical methods of differential geometry, we define invariants of non-developable ruled surfaces in Euclidean 3-space, called structure functions, and show kinematics meaning of these invariants. We also generalize the notion of the angle of pitch of a closed ruled surface to any non-developable ruled surface. Then we discuss the properties of these invariants and give a kind of classification of the non-developable ruled surfaces in Euclidean 3-space with the theories of these invariants.

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Authors and Affiliations

  1. Department of Mathematics, Northeastern University, Shenyang, 110004, People’s Republic of China

    Huili Liu & Yanhua Yu

  2. Department of Mathematics, Jeju National University, Jeju, 690-756, Korea

    Seoung Dal Jung

Authors
  1. Huili Liu
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  2. Yanhua Yu
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  3. Seoung Dal Jung
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Corresponding author

Correspondence to Huili Liu.

Additional information

This study was supported by NSFC (No. 11071032 and 11371080); Joint Research of NSFC and NRF (No. 11111140377). H. Liu was Partially supported by Chern Institute of Mathematics and Northeastern University. S. D. Jung was supported by NRF-2011-616-C00040.

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Liu, H., Yu, Y. & Jung, S.D. Invariants of non-developable ruled surfaces in Euclidean 3-space. Beitr Algebra Geom 55, 189–199 (2014). https://doi.org/10.1007/s13366-013-0177-z

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  • DOI: https://doi.org/10.1007/s13366-013-0177-z

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