Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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KINEMATICAL INVARIANTS AND APPLICATIONS FOR SURFACES IN THREE DIMENSIONAL EUCLIDEAN SPACE

  • Seoung Dal Jung (Department of Mathematics and Research Institute for Basic Sciences Jeju National University) ;
  • Huili Liu (Department of Mathematics Northeastern University) ;
  • Yixuan Liu (College of Life Sciences Peking University)
  • Received : 2023.11.07
  • Accepted : 2024.03.12
  • Published : 2024.07.31
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Abstract

In three dimensional Euclidean space we consider kinematical invariants of the surface which is generated by the motion of a planar curve, especially, the surface which is foliated by circles. At first we characterize the properties of single parameter plane with the theories of unit spherical curve in three dimensional Euclidean space. Then using these results we give the invariants and differential invariants, kinematical properties and some special examples of the surface foliated by circles. The methods established here can be used to the other kinds of the surface in three dimensional Euclidean space.

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Acknowledgement

Supported by National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NRF-2018R1A2B2002046). Partially supported by NSFC; Joint Research of NSFC and NRF; Chern Institute of Mathematics and Northeastern University.

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