h-Principles for curves and knots of constant curvature
نویسندگان
چکیده
منابع مشابه
h-PRINCIPLES FOR CURVES AND KNOTS OF CONSTANT CURVATURE
We prove that C∞ curves of constant curvature satisfy, in the sense of Gromov, the relative C-dense h-principle in the space of immersed curves in Euclidean space Rn≥3. In particular, in the isotopy class of any given C knot f there exists a C∞ knot e f of constant curvature which is C-close to f . More importantly, we show that if f is C, then the curvature of e f may be set equal to any const...
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Charles Evans We present an exposition of various results dealing with the total curvature of curves in Euclidean 3-space. There are two primary results: Fenchel’s theorem and the theorem of Fary and Milnor. Fenchel’s theorem states that the total curvature of a simple closed curve is greater than or equal to 2π, with equality if and only if the curve is planar convex. The Fary-Milnor theorem s...
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In the euclidean plane, a regular curve can be defined through its intrinsic equation which relates its curvature k to the arc length s. Elastic plane curves were determined this way. If k(s) = 2α cosh(αs) , the curve is known by the name “la courbe des forçats”, introduced in 1729 by Giovanni Poleni in relation with the tractrix [9]. The above equation is yet meaningful on a surface if one int...
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In this paper, we consider the isoptic curves in 2-dimensional geometries of constant curvature E, H, E. The topic is widely investigated in the Euclidean plane E, see for example [1] and [15] and the references given there. In the hyperbolic and elliptic plane (according to [18]), there are few results in this topic (see [3] and [4]). In this paper, we give a review of the known results on iso...
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ژورنال
عنوان ژورنال: Geometriae Dedicata
سال: 2007
ISSN: 0046-5755,1572-9168
DOI: 10.1007/s10711-007-9151-y