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Ruled invariants and total classification of non-developable ruled surfaces

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Abstract

In this paper we give the necessary and sufficient condition of which a ruled surface is the principal normal ruled surface of a space curve using the theories of ruled invariants of ruled surface in three dimensional Euclidean space. Then for the ruled surfaces in three dimensional Euclidean space we describe their geometric structures and obtain total classifications. Since the ruled surfaces are the simplest foliated submanifolds, our effective and elementary methods can be used to reveal the properties and structures of the Riemannian foliations and foliated submanifolds.

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Authors and Affiliations

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

    Huili Liu

  2. College of Life Sciences, Peking University, Beijing, 100871, People’s Republic of China

    Yixuan Liu

  3. Department of Mathematics and Research Institute for Basic Sciences, Jeju National University, Jeju, 690-756, Korea

    Seoung Dal Jung

Authors
  1. Huili Liu
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  2. Yixuan Liu
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  3. Seoung Dal Jung
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Correspondence to Huili Liu.

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The authors declare no conflict of interests. All data are inclued in this manuscript.

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Huili Liu: Supported by NSFC; Joint Research of NSFC and NRF; Chern Institute of Mathematics and Northeastern University.

Seoung Dal Jung: Supported by National Research Foundation of Korea (NRF) Grant funded by the Korea Government (MSIP) (NRF-2018R1A2B2002046)

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Liu, H., Liu, Y. & Jung, S.D. Ruled invariants and total classification of non-developable ruled surfaces. J. Geom. 113, 21 (2022). https://doi.org/10.1007/s00022-022-00631-9

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  • DOI: https://doi.org/10.1007/s00022-022-00631-9

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