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Integrable Flows for Starlike Curves in Centroaffine Space  [cached]
Annalisa Calini,Thomas Ivey,Gloria Marí Beffa
Symmetry, Integrability and Geometry : Methods and Applications , 2013,
Abstract: We construct integrable hierarchies of flows for curves in centroaffine R^3 through a natural pre-symplectic structure on the space of closed unparametrized starlike curves. We show that the induced evolution equations for the differential invariants are closely connected with the Boussinesq hierarchy, and prove that the restricted hierarchy of flows on curves that project to conics in RP^2 induces the Kaup-Kuperschmidt hierarchy at the curvature level.
Integrable Flows for Starlike Curves in Centroaffine Space  [PDF]
Annalisa Calini,Thomas Ivey,Gloria Mari Beffa
Physics , 2013, DOI: 10.3842/SIGMA.2013.022
Abstract: We construct integrable hierarchies of flows for curves in centroaffine ${\mathbb R}^3$ through a natural pre-symplectic structure on the space of closed unparametrized starlike curves. We show that the induced evolution equations for the differential invariants are closely connected with the Boussinesq hierarchy, and prove that the restricted hierarchy of flows on curves that project to conics in ${\mathbb{RP}}^2$ induces the Kaup-Kuperschmidt hierarchy at the curvature level.
On the ring of invariants of ordinary quartic curves in characteristic 2  [PDF]
Juergen Mueller,Christophe Ritzenthaler
Mathematics , 2004,
Abstract: In this article a complete set of invariants for ordinary quartic curves in characteristic 2 is computed.
The motivic Donaldson-Thomas invariants of (-2) curves  [PDF]
Ben Davison,Sven Meinhardt
Mathematics , 2012,
Abstract: In this paper we calculate the motivic Donaldson--Thomas invariants for (-2)-curves arising from 3-fold flopping contractions in the minimal model programme. We translate this geometric situation into the machinery developed by Kontsevich and Soibelman, and using the results and framework of the authors' previous work we describe the monodromy on these invariants. In particular, in contrast to all existing known Donaldson-Thomas invariants for small resolutions of Gorenstein singularities these monodromy operations are nontrivial.
INVOLUTE CURVES OF BIHARMONIC CURVES IN SL2(R)  [PDF]
TALAT KORPINAR,VEDAT ASIL,ESSIN TURHAN
Journal of Science and Arts , 2011,
Abstract: . In this paper, we study involute curves of biharmonic curves in the SL2(R). Finally, we find out their explicit parametric equations.
Restricting Fourier transforms of measures to curves in R^2  [PDF]
M. Burak Erdogan,Daniel M. Oberlin
Mathematics , 2010,
Abstract: We establish estimates for restrictions to certain curves in R^2 of the Fourier transforms of some fractal measures.
Pairs of pants, Pochhammer curves and $L^2$-invariants  [PDF]
Marcel B?kstedt,Nuno M. Rom?o
Mathematics , 2014,
Abstract: We propose an intuitive interpretation for nontrivial $L^2$-Betti numbers of compact Riemann surfaces in terms of certain loops in embedded pairs of pants. This description uses twisted homology associated to the Hurewicz map of the surface, and it satisfies a sewing property with respect to a large class of pair-of-pants decompositions. Applications to supersymmetric quantum mechanics incorporating Aharonov-Bohm phases are briefly discussed, for both point particles and topological solitons (abelian and non-abelian vortices) in two dimensions.
Differential Invariants of SL(2) and SL(3)-ACTIONS on R^2  [PDF]
Mehdi Nadjafikhah,Seyed-Reza Hejazi
Mathematics , 2007,
Abstract: The main purpose of this paper is calculation of differential invariants which arise from prolonged actions of two Lie groups SL(2) and SL(3) on the $n$th jet space of $R^2$. It is necessary to calculate $n$th prolonged infenitesimal generators of the action.
On the biharmonic curves in the special linear group $SL(2,R)$  [PDF]
I. I. Onnis,A. Passos Passamani
Mathematics , 2014,
Abstract: We characterize the biharmonic curves in the special linear group $SL(2,R)$. In particular, we show that all proper biharmonic curves in $SL(2,R)$are helices and we give their explicit parametrizations as curves in the pseudo-Euclidean space $R^4_2$.
Boundary value problems for Willmore curves in $\mathbb{R}^2$  [PDF]
Rainer Mandel
Mathematics , 2015,
Abstract: In this paper the Navier problem and the Dirichlet problem for Willmore curves in $\mathbb{R}^2$ is solved.
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