대한수학회지 (Journal of the Korean Mathematical Society)

  • 제58권6호
  • /
  • Pages.1485-1500
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  • 2021
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  • 0304-9914(pISSN)
  • /
  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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CURVES ORTHOGONAL TO A VECTOR FIELD IN EUCLIDEAN SPACES

  • da Silva, Luiz C.B. (Department of Physics of Complex Systems Weizmann Institute of Science) ;
  • Ferreira, Gilson S. Jr. (Department of Mathematics Federal Rural University of Pernambuco)
  • 투고 : 2021.02.18
  • 심사 : 2021.06.04
  • 발행 : 2021.11.01
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초록

A curve is rectifying if it lies on a moving hyperplane orthogonal to its curvature vector. In this work, we extend the main result of [Chen 2017, Tamkang J. Math. 48, 209] to any space dimension: we prove that rectifying curves are geodesics on hypercones. We later use this association to characterize rectifying curves that are also slant helices in three-dimensional space as geodesics of circular cones. In addition, we consider curves that lie on a moving hyperplane normal to (i) one of the normal vector fields of the Frenet frame and to (ii) a rotation minimizing vector field along the curve. The former class is characterized in terms of the constancy of a certain vector field normal to the curve, while the latter contains spherical and plane curves. Finally, we establish a formal mapping between rectifying curves in an (m + 2)-dimensional space and spherical curves in an (m + 1)-dimensional space.

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과제정보

L. C. B. da Silva would like to thank the financial support provided by the Mora Miriam Rozen Gerber fellowship for Brazilian postdocs.

참고문헌

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