Computation of the Bennequin invariant of a Legendre curve from the geometry of its front

1989 ◽  
Vol 22 (3) ◽  
pp. 246-248 ◽  
Author(s):  
S. L. Tabachnikov
Keyword(s):  
Legendre Curve

scholarly journals On interpolating sesqui-harmonic Legendre curves in Sasakian space forms

2019 ◽  
Vol 17 (01) ◽  
pp. 2050005 ◽  
Author(s):  
Fatma Karaca ◽  
Cihan Özgür ◽  
Uday Chand De
Keyword(s):  
Space Form ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sasakian Space Form ◽  
Space Forms ◽  
Legendre Curve ◽  
Sasakian Space Forms ◽  
Legendre Curves ◽  
Necessary And Sufficient

We consider interpolating sesqui-harmonic Legendre curves in Sasakian space forms. We find the necessary and sufficient conditions for Legendre curves in Sasakian space forms to be interpolating sesqui-harmonic. Finally, we obtain a proper example for an interpolating sesqui-harmonic Legendre curve in a Sasakian space form.

scholarly journals Framed curves in the Euclidean space

2016 ◽  
Vol 16 (3) ◽  
Author(s):  
Shun’ichi Honda ◽  
Masatomo Takahashi
Keyword(s):  
Euclidean Space ◽  
Tangent Bundle ◽  
Moving Frame ◽  
Regular Curve ◽  
Smooth Functions ◽  
Independent Condition ◽  
Legendre Curve ◽  
Space Curves ◽  
Unit Tangent Bundle ◽  
Legendre Curves

AbstractA framed curve in the Euclidean space is a curve with a moving frame. It is a generalization not only of regular curves with linear independent condition, but also of Legendre curves in the unit tangent bundle. We define smooth functions for a framed curve, called the curvature of the framed curve, similarly to the curvature of a regular curve and of a Legendre curve. Framed curves may have singularities. The curvature of the framed curve is quite useful to analyse the framed curves and their singularities. In fact, we give the existence and the uniqueness for the framed curves by using their curvature. As applications, we consider a contact between framed curves, and give a relationship between projections of framed space curves and Legendre curves.

Cyclotomic problem, Gauss sums and Legendre curve

2013 ◽  
Vol 56 (7) ◽  
pp. 1485-1508 ◽  
Author(s):  
LingLi Xia ◽  
Jing Yang
Keyword(s):  
Gauss Sums ◽  
Legendre Curve

scholarly journals Explicit points on the Legendre curve III

2014 ◽  
Vol 8 (10) ◽  
pp. 2471-2522 ◽  
Author(s):  
Douglas Ulmer
Keyword(s):  
Legendre Curve

scholarly journals LEGENDRE CURVES ON 3-DIMENSIONAL f-KENMOTSU MANIFOLDS ADMITTING SCHOUTEN-VAN KAMPEN CONNECTION

2020 ◽  
pp. 357
Author(s):  
Ashis Mondal
Keyword(s):  
Three Dimensional ◽  
Kenmotsu Manifold ◽  
3 Dimensional ◽  
Legendre Curve ◽  
Kenmotsu Manifolds ◽  
Legendre Curves ◽  
Slant Curves

In the present paper, biharmonic Legendre curves with respect to Schouten-Van Kampen connection have been studied on three-dimensional f-Kenmotsu manifolds. Locally $\phi $-symmetric Legendre curves on three-dimensional f-Kenmotsu manifolds with respect to Schouten-Van Kampen Connection have been introduced.Also slant curves have been studied on three-dimensional f-Kenmotsu manifolds with respect to Schouten-Van Kampen connection. Finally, we constract an example of a Legendre curve in a 3-dimensional f-Kenmotsu manifold.

scholarly journals C-parallel and C-proper slant curves of S-manifolds

Filomat ◽  
2019 ◽  
Vol 33 (19) ◽  
pp. 6305-6313
Author(s):  
Şaban Güvenç ◽  
Cihan Özgür
Keyword(s):  
Normal Bundle ◽  
Legendre Curve ◽  
Slant Curve ◽  
Slant Helix ◽  
Slant Curves

In the present paper, we define and study C-parallel and C-proper slant curves of S-manifolds. We prove that a slant curve in an S-manifold of order r ? 3, under certain conditions, is C-parallel or C-parallel in the normal bundle if and only if it is a non-Legendre slant helix or Legendre helix, respectively. Moreover, under certain conditions, we show that is C-proper or C-proper in the normal bundle if and only if it is a non-Legendre slant curve or Legendre curve, respectively. We also give two examples of such curves in R2m+s(-3s).

scholarly journals Legendre Matrix Method for Legendre Curve in Sasakian 3-Manifold

2021 ◽  
Vol 46 (3) ◽  
pp. 205-219
Author(s):  
Tuba Ağirman Aydin ◽  
Mehmet Sezer ◽  
Hüseyin Kocayiğit
Keyword(s):  
Approximate Solution ◽  
Differential Equations ◽  
Collocation Method ◽  
Matrix Method ◽  
Geometric Properties ◽  
Legendre Curve ◽  
Unit Speed ◽  
Sample Application ◽  
Legendre Curves ◽  
Study Unit

Abstract In this study, unit-speed the Legendre curves are studied in Sasakian 3-manifold. Firstly, differential equations characterizing the Legendre curves are obtained and the method used for the approximate solution is explained. Then, the approximate solution is found for one of the characterizations of the Legendre curve with the Legendre matrix collocation method. In addition, a sample application is made to make the method more understandable. And finally, with the help of these equations and the approximate solution, the geometric properties of this curve type are examined.

scholarly journals Variance of sums in arithmetic progressions of divisor functions associated with higher degree L-functions in 𝔽q[t]

2019 ◽  
Vol 16 (05) ◽  
pp. 1013-1030
Author(s):  
Edva Roditty-Gershon ◽  
Chris Hall ◽  
Jonathan P. Keating
Keyword(s):  
Elliptic Curves ◽  
Conjugacy Classes ◽  
Arithmetic Progressions ◽  
Divisor Function ◽  
Legendre Curve ◽  
Divisor Functions ◽  
Matrix Integrals ◽  
Usual Formula ◽  
Special Case

We compute the variances of sums in arithmetic progressions of generalized [Formula: see text]-divisor functions related to certain [Formula: see text]-functions in [Formula: see text], in the limit as [Formula: see text]. This is achieved by making use of recently established equidistribution results for the associated Frobenius conjugacy classes. The variances are thus expressed, when [Formula: see text], in terms of matrix integrals, which may be evaluated. Our results extend those obtained previously in the special case corresponding to the usual [Formula: see text]-divisor function, when the [Formula: see text]-function in question has degree one. They illustrate the role played by the degree of the [Formula: see text]-functions; in particular, we find qualitatively new behavior when the degree exceeds one. Our calculations apply, for example, to elliptic curves defined over [Formula: see text], and we illustrate them by examining in some detail the generalized [Formula: see text]-divisor functions associated with the Legendre curve.

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