On the generalized helices of Hayden and Sypták in an N-space
1941 ◽
Vol 37
(3)
◽
pp. 229-243
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In this paper we are concerned with curves (C) of the following types:where k1, k2, …, kh−1, kh = 0 (h ≤ n) are the curvatures of (C) relative to the space Vn in which (C) lie. Hayden proved that a curve in a Vn is an (A)2m, h = 2m + 1, if and only if it admits an auto-parallel vector along it which lies in the osculating space of the curve and makes constant angles with the tangent and the principal normals. Independently, Sypták∥ stated without proof that a curve in an Rn is a (B)n if and only if it admits a certain number of fixed R2's having the same angle properties; he also gave to such a curve a set of canonical equations from which many interesting properties follow as immediate consequences.
1969 ◽
Vol 27
◽
pp. 160-161
1983 ◽
Vol 41
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pp. 708-709
1974 ◽
Vol 32
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pp. 436-437
1978 ◽
Vol 36
(1)
◽
pp. 548-549
◽
1978 ◽
Vol 36
(1)
◽
pp. 540-541
1978 ◽
Vol 36
(1)
◽
pp. 456-457
1988 ◽
Vol 46
◽
pp. 218-219
1978 ◽
Vol 36
(1)
◽
pp. 176-177
Keyword(s):
1972 ◽
Vol 30
◽
pp. 398-399
Keyword(s):
1988 ◽
Vol 46
◽
pp. 822-823