A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Derives a new first order differential equation for smooth surfaces.
We show how the rotation and translation fields of a surface, introduced by G. Darboux, may be used to obtain short proofs of a well-known theorem (that reads that the total mean curvature of a surface is stationary under an infinitesimal bending) and a new theorem (that reads that every infinitesimal flex of any simpl…
In this study, we defined Fermi-Walker derivative in Galilean space . Fermi-Walker transport and non-rotating frame by using Fermi- Walker derivative are given in . Being conditions of Fermi-Walker transport and non-rotating frame are investigated along any curve for Frenet frame and Darboux…
Sequences of Levy transformations for the Darboux system of conjugates nets in multidimensions are studied. We show that after a suitable number of Levy transformations, with at least a Levy transformation in each direction, we get closed formulae in terms of multi-Wroński determinants. These formulae are for the tange…
The paper extends classical Darboux theorems to various geometric structures in field theories.
The paper studies geometric properties of soliton surfaces using an extended Darboux frame field.
For a regular curve on a spacelike surface in Lorentz-Minkowski -space, we have a moving frame along the curve which is called a Lorentzian Darboux frame. We introduce five special vector fields along the curve associated to the Lorentzian Darboux frame and investigate their singularities.
Classifies Lie bialgebras using Darboux families.
New approach to rotational Weingarten surfaces using geometric momentum.
Generalizes Riemann's results on flat coordinates for non-symmetric bilinear forms.
A new transform links rotating calorons to solutions of a differential equation.
The study characterizes helices in Euclidean and hyperbolic spaces.
In his monograph "Leçons sur les systèmes orthogonaux et les coordonnées curvilignes. Principes de géométrie analytique", 1910, Darboux stated three theorems providing local existence and uniqueness of solutions to first order systems of the type \[\partial_{x_i} u_α(x)=f^α_i(x,u(x)),\quad i\in I_α\subseteq\{1,\dots,n\…
In this paper, we study spherical images of the modified orthogonal vector fields and Darboux vector of a regular curve which lies on the unit sphere in Euclidean 3-space.
We state some generalizations of a theorem due to G. Darboux, which originally states that a polynomial vector field in the complex plane exhibits a rational first integral and has all its orbits algebraic provided that it exhibits infinitely many algebraic orbits. In this paper, we give an interpretation of this resul…
We analyze Darboux transformations in very general settings for multidimensional linear partial differential operators. We consider all known types of Darboux transformations, and present a new type. We obtain a full classification of all operators that admit Wronskian type Darboux transformations of first order and a …
The paper extends a theorem for complex structures on Lie groups to Courant algebroids.
Rotates MFVI for better Gaussian approximations.
In this note we prove that an analytic symplectic action of a semisimple Lie algebra can be locally linearized in Darboux coordinates. This result yields simultaneous analytic linearization for Hamiltonian vector fields in a neighbourhood of a common zero. We also provide an example of smooth non-linearizable Hamiltoni…
The paper proves conditions for Darboux integrability in diagonal hydrodynamic systems.
The paper is devoted to vector fields on the spaces R^2 and R^3, their flow and invariants. Attention is plaid on the tensor representations of the group GL(2,R) and on fundamental vector fields. The rotation group on R^3 is generalized to rotation groups with arbitrary quadrics as orbits.
We define general rotational surfaces of elliptic and hyperbolic type in the pseudo-Euclidean 4-space with neutral metric which are analogous to the general rotational surfaces of C. Moore in the Euclidean 4-space. We study Lorentz general rotational surfaces with plane meridian curves and give the complete classificat…
Investigates Darboux rectifying curves on smooth surfaces.
We study an analogue of the classical Bianchi-Darboux transformation for L-isothermic surfaces in Laguerre geometry, the Bianchi-Darboux transformation. We show how to construct the Bianchi-Darboux transforms of an L-isothermic surface by solving an integrable linear differential system. We then establish a permutabili…
Introduces Darboux-Lie derivative for fiber bundles.
The paper explores unique properties of Darboux transformations of spacelike curves in the Lorentz-Minkowski plane.
Darboux inverses explain Kepler orbits on curved surfaces.
In this study, we introduce Darboux slant ruled surfaces in the Euclidean 3-space which is defined by the property that the Darboux vector of orthonormel frame of ruled surface makes a constant angle with a fixed, non-zero direction. We obtain the characterizations of Darboux slant ruled surfaces regarding the conical …
We prove that a normal vector field along a curve in R3 is rotation minimizing (RM) if and only if it is parallel respect to the normal connection. This allows us to generalize all the results of RM vectors and frames to curves immersed in Riemannian manifolds.
The paper classifies surfaces with constant skew curvature in 3-space forms.
We give a full description of Darboux transformations of any order for arbitrary (nondegenerate) differential operators on the superline. We show that every Darboux transformation of such operators factorizes into elementary Darboux transformations of order one. Similar statement holds for operators on the ordinary lin…
The paper discusses a new method for constructing two-step Darboux transforms of isothermic surfaces.
We generalize the notions of the Futaki invariant and extremal vector field of a compact Kähler manifold to the general almost-Kahler case and show the periodicity of the extremal vector field when the symplectic form represents an integral cohomology class modulo torsion. We also give an explicit formula of the hermit…
The paper classifies solitons in a curved product space.
In the four-dimensional pseudo-Euclidean space with neutral metric there are three types of rotational surfaces with two-dimensional axis - rotational surfaces of elliptic, hyperbolic or parabolic type. A surface whose mean curvature vector field is lightlike is said to be quasi-minimal. In this paper we classify all q…
We define a transformation on harmonic maps from a Riemann surface into the 2-sphere which depends on a complex parameter, the so-called mu-Darboux transformation. In the case when the harmonic map N is the Gauss map of a constant mean curvature surface f and the parameter is real, the mu-Darboux transformation of -N i…
Study on surfaces with constant curvature under a specific connection.
New method linearizes Darboux transformations of discrete curves.
Introduces homogeneity supermanifolds for studying graded structures.
In this study, we give definitions and characterizations of eikonal slant helices, eikonal Darboux helices and non-normed eikonal Darboux helices in 3-dimensional pseudo- Riemannian manifold M . We show that every eikonal slant helix is also an eikonal Darboux helix for timelike and spacelike curves. Furthermore, we ob…
In this paper, we consider a regular curve on an oriented surface in Euclidean 3-space with the Darboux frame along the curve, where is the unit tangent vector field of the curve, is the surface normal restricted to the curve and $\mathsf{V}=\mathsf{U}\ti…
In this study, we give definitions and characterizations of eikonal slant helix curves, eikonal Darboux helices and non-normed eikonal Darboux helices in three dimensional Riemannian manifold 3 M . We show that every eikonal slant helix is also an eikonal Darboux helix. Furthermore, we obtain that if the curve a is a n…
Study of timelike surfaces in Minkowski space with specific geometric properties.
Darboux Wronskian formulas allow to construct Darboux transformations, but Laplace transformations, which are Darboux transformations of order one cannot be represented this way. It has been a long standing problem on what are other exceptions. In our previous work we proved that among transformations of total order on…
New CMC surfaces with dihedral symmetry constructed from Darboux transforms.
The normal map of curves is analyzed as a vector field on a cylinder.
Rotation minimizing vector fields and frames were introduced by Bishop as an alternative to the Frenet frame. They are used in CAGD because they can be defined even the curvature vanishes. Nevertheless, many other geometric properties have not been studied. In the present paper, RM vector fields along a curve immersed …
TURB-Rot provides a large database of turbulent rotating flow snapshots for research.