On Helices in the Euclidean $n$-Space.
نویسندگان
چکیده
منابع مشابه
Slant Helices in Euclidean 4-space E
We consider a unit speed curve α in Euclidean four-dimensional space E and denote the Frenet frame by {T,N,B1,B2}. We say that α is a slant helix if its principal normal vector N makes a constant angle with a fixed direction U . In this work we give different characterizations of such curves in terms of their curvatures. MSC: 53C40, 53C50
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متن کاملSome Characterizations of Slant Helices in the Euclidean Space E
In this work, the notion of a slant helix is extended to the space E. First, we introduce the type-2 harmonic curvatures of a regular curve. Thereafter, by using this, we present some necessary and sufficient conditions for a curve to be a slant helix in Euclidean n-space. We also express some integral characterizations of such curves in terms of the curvature functions. Finally, we give some c...
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Inclined curves or so-called general helices are well-known curves in the classical differential geometry of space curves [9] and we refer to the reader for recent works on this type of curves [6, 12]. Recently, Izumiya and Takeuchi have introduced the concept of slant helix in Euclidean 3-space E saying that the normal lines makes a constant angle with a fixed direction [7]. They characterize ...
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The theory of the isoptic curves is widely studied in the Euclidean plane E2 (see [1] and [13] and the references given there). The analogous question was investigated by the authors in the hyperbolic H2 and elliptic E2 planes (see [3], [4]), but in the higher dimensional spaces there is no result according to this topic. In this paper we give a natural extension of the notion of the isoptic cu...
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ژورنال
عنوان ژورنال: MATHEMATICA SCANDINAVICA
سال: 1974
ISSN: 1903-1807,0025-5521
DOI: 10.7146/math.scand.a-11543