共查询到20条相似文献,搜索用时 31 毫秒
1.
We give a moving frame of a Legendre curve (or, a frontal) in the unit tangent bundle and define a pair of smooth functions of a Legendre curve like as the curvature of a regular plane curve. It is quite useful to analyse the Legendre curves. The existence and uniqueness for Legendre curves hold similarly to the case of regular plane curves. As an application, we consider contact between Legendre curves and the arc-length parameter of Legendre immersions in the unit tangent bundle. 相似文献
2.
MA Renyi 《数学年刊B辑(英文版)》1999,20(4):425-434
61.IntroductionandandResultsWefirstrecallseveraldefinitionsin[1].Acontactstructtireonamanifoldisafieldofatangenthyperplanes(contacthyperplanes)thatis"nondegenerate"atanypoiflt,local1ysuchafieldisdefinedasthefieldofzerosofal-formcr,calledacontactform.Thenondegeneracy.conditionisthatdcrisnondegenerateonthehyperplanesonwhichcrvanishes,equivalently,in(2n l)-space:aA(da)"/o.Theimportantexampleofcontactmanifoldisthewell-knownprojectivecotangentbundlesdefindedaJsfollows:LetN=T*Mbethecotangentbundl… 相似文献
3.
MA Renyi 《数学年刊A辑(中文版)》1999,20(4):425-434
The author first proves the existences of $J-$holomorphic curves in
the symplectizations of Legendre fibrations and then as
an application confirms the Weinstein conjectures
on contact manifolds of Legendre fibrations. As a corollary,
a new proof on the theorem due to Hofer, Viterbo, Gluck, Ziller,
Weinstein and Ljusternik-Fet Theorem is provided, which
is quite different from their original proofs. 相似文献
4.
Jeremy Rouse 《The Ramanujan Journal》2006,12(2):197-205
We provide uniform formulas for the real period and the trace of Frobenius associated to an elliptic curve in Legendre normal
form. These are expressed in terms of classical and Gaussian hypergeometric functions, respectively.
2000 Mathematics Subject Classification Primary—11G05, 33C05
This research was supported by K. Ono’s NSF grant 相似文献
5.
Ukrainian Mathematical Journal - We represent Legendre curves in unit tangent bundle by using rotation minimizing vector fields. Ruled surfaces corresponding to these curves are specified. The... 相似文献
6.
WU HongFeng & FENG RongQuan College of Science North China University of technology Beijing China LMAM School of Mathematical Sciences Peking University Beijing 《中国科学 数学(英文版)》2011,(9)
In this paper,the number of isomorphism classes of Legendre elliptic curves over finite field is enumerated. 相似文献
7.
Because of the limitation of the manufacturing technology, initial stress in functionally graded materials (FGM) and structures is inevitable. Based on the theory of “Mechanics of Incremental Deformations”, the guided wave propagation in FGM plates under gravity, homogeneous initial stress in the thickness direction and inhomogeneous initial stress in the wave propagation direction is investigated. The Legendre polynomial series method is used to solve the coupled wave equations with variable coefficients. The convergence of the polynomial series method is discussed through the numerical examples. The effects of the initial stress on the Lamb-like wave and on the SH wave are investigated respectively and the numerical results show they are quite distinct. The effect of the gravity on the wave propagation can be ignored. The effects of the initial stress in the thickness direction are very different from those of the initial stress in the wave propagation direction, both on the dispersion curves and on the displacement and stress distributions. 相似文献
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9.
It is first observed that on a 3-dimensional Sasakian manifold the torsion of a Legendre curve is identically equal to +1. It is then shown that, conversely, if a curve on a Sasakian 3-manifold has constant torsion +1 and satisfies the initial conditions at one point for a Legendre curve, it is a Legendre curve. Furthermore, among contact metric structures, this property is characteristic of Sasakian metrics. For the standard contact structure onR
3 with its standard Sasakian metric the curvature of a Legendre curve is shown to be twice the curvature of its projection to thexy-plane with respect to the Euclidean metric. Thus this metric onR
3 is more natural for the study of Legendre curves than the Euclidean metric.This work was done while the first author was a visiting scholar at Michigan State University. 相似文献
10.
A sphere of dimension 4n+3 admits three Sasakian structures and it is natural to ask if a submanifold can be an integral submanifold for more than one of the contact structures. In the 7-sphere it is possible to have curves which are Legendre curves for all three contact structures and there are 2 and 3-dimensional submanifolds which are integral submanifolds of two of the contact structures. One of the results here is that if a 3-dimensional submanifold is an integral submanifold of one of the Sasakian structures and invariant with respect to another, it is an integral submanifold of the remaining structure and is a principal circle bundle over a holmophic Legendre curve in complex projective 3-space. 相似文献
11.
SCOTT NOLLET 《Compositio Mathematica》1997,106(2):203-210
In this paper we construct smooth irreducible spacecurves C which link geometrically by surfaces of minimal degree containingC to curves of generic embedding dimension three. This produces interesting behavior with respect to both C and . The curves link to smooth connected curves by surfaces of low degree butcannot link to smooth connected curves by surfaces of high degree.The curves C give counterexamples to a conjecture of Martin-Deschamps and Perrin. 相似文献
12.
Stefan Kebekus 《Mathematische Nachrichten》2002,242(1):119-131
Classification theory and the study of projective varieties which are covered by rational curves of minimal degrees naturally leads to the study of families of singular rational curves. Since families of arbitrarily singular curves are hard to handle, it has been shown in [Keb00] that there exists a partial resolution of singularities which transforms a bundle of possibly badly singular curves into a bundle of nodal and cuspidal plane cubics. In cases which are of interest for classification theory, the total spaces of th se bundles will clearly be projective. It is, however, generally false that an arbitrary bundle of plane cubics is globally projective. For that reason the question of projectivity and the study of moduli seems to be of interest, and the present work gives a characterization of the projective bundles. 相似文献
13.
Robert S. Rumely 《Journal of Number Theory》1983,17(3):389-402
A formula for the grössencharacter of an elliptic curve with complex multiplication, in a family parametrized by modified Weierstrass functions or classical theta-functions, is given. The method is based on Shimura's Reciprocity Law for modular functions, and applies to Legendre, Jacobi, and Hesse curves. As an application, the conductors of the CM curves in these families are determined. 相似文献
14.
15.
In this paper, we determine zeta-functions of some curves of genus 3 over finite fields by gluing three elliptic curves based on Xing's research, and the examples show that there exists a maximal curve of genus 3 over F49. 相似文献
16.
In their seminal paper, Miyaji et al. [13] describe a simple method for the creation of elliptic curves of prime order with
embedding degree 3, 4, or 6. Such curves are important for the realisation of pairing-based cryptosystems on ordinary (non-supersingular)
elliptic curves. We provide an alternative derivation of their results, and extend them to allow for the generation of many
more suitable curves.
Research supported by Enterprise Ireland grant IF/2002/0312/N. 相似文献
17.
Pavlos Tzermias 《Transactions of the American Mathematical Society》2004,356(3):939-951
We investigate low-degree points on the Fermat curve of degree 13, the Snyder quintic curve and the Klein quartic curve. We compute all quadratic points on these curves and use Coleman's effective Chabauty method to obtain bounds for the number of cubic points on each of the former two curves.
18.
19.
D. Fetcu C. Oniciuc 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》2007,77(1):179-190
We obtain the parametric equations of all biharmonic Legendre curves and Hopf cylinders in the 3-dimensional unit sphere endowed with the modified Sasakian structure defined byTanno. 相似文献
20.
Dawei Chen 《Advances in Mathematics》2011,(2):1135
We study the algebro-geometric aspects of Teichmüller curves parameterizing square-tiled surfaces with two applications.(a) There exist infinitely many rigid curves on the moduli space of hyperelliptic curves. They span the same extremal ray of the cone of moving curves. Their union is a Zariski dense subset. Hence they yield infinitely many rigid curves with the same properties on the moduli space of stable n-pointed rational curves for even n.(b) The limit of slopes of Teichmüller curves and the sum of Lyapunov exponents for the Teichmüller geodesic flow determine each other, which yields information about the cone of effective divisors on the moduli space of curves. 相似文献