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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 대한수학회 대한수학회지 대한수학회지 제58권 제6호
- 발행연도
- 2021.11
- 수록면
- 1,485 - 1,500 (16page)
- DOI
- 10.4134/JKMS.j210119
이용수
초록· 키워드
오류제보하기
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. {\bf 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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참고문헌 (17)
참고문헌 신청
B. Altunkaya / 2016 / On rectifying slant helices in Euclidean 3-space / Konuralp J. Math 4(2):17~24
Richard L. Bishop / 1975 / There is More than One Way to Frame a Curve / The American Mathematical Monthly 82(3):246
Stijn CAMBIE / 2016 / Rectifying curves in the $n$-dimensional Euclidean space / TURKISH JOURNAL OF MATHEMATICS 40:210~223
Bang-Yen Chen / 2003 / When Does the Position Vector of a Space Curve Always Lie in Its Rectifying Plane? / The American Mathematical Monthly 110(2):147
Bang-Yen Chen / 2017 / Rectifying curves and geodesics on a cone in the Euclidean 3-space / Tamkang Journal of Mathematics 48(2):209~214
Richard L. Bishop / 1975 / There is More than One Way to Frame a Curve / The American Mathematical Monthly 82(3):246
Stijn CAMBIE / 2016 / Rectifying curves in the $n$-dimensional Euclidean space / TURKISH JOURNAL OF MATHEMATICS 40:210~223
Bang-Yen Chen / 2003 / When Does the Position Vector of a Space Curve Always Lie in Its Rectifying Plane? / The American Mathematical Monthly 110(2):147
Bang-Yen Chen / 2017 / Rectifying curves and geodesics on a cone in the Euclidean 3-space / Tamkang Journal of Mathematics 48(2):209~214
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