Related papers: Vector fields and genus in dimension 3
In this paper, we show that for given Bernoulli function and entropy function at the upstream, if the incoming mass flux is within a suitable range, then there exists a unique outer pressure such that smooth subsonic three-dimensional…
We prove an existence result for solutions to the stationary Euler equations in a domain with nonsmooth boundary. This is an extension of a previous existence result in smooth domains by Alber (1992). The domains we consider have a boundary…
The dynamics of two-dimensional three-component (2D3C) flows is relevant to describe the long-time evolution of strongly rotating flows and/or of conducting fluids with a strong mean magnetic field. We show that in the presence of a strong…
We prove that the geodesic flow on the unit tangent bundle to a hyperbolic 2-orbifold is left-handed if and only if the orbifold is a sphere with three conic points. As a consequence, on the unit tangent bundle to a 3-conic sphere, the lift…
An explicit expression is obtained for the sectional curvature in the plane spanned by two stationary flows, cos(k, x) and cos(l, x). It is shown that for certain values of the wave vectors k and l the curvature becomes positive for alpha >…
In this article we study the spectrum of totally geodesic surfaces of a finite volume hyperbolic 3-manifold. We show that for arithmetic hyperbolic 3-manifolds that contain a totally geodesic surface, this spectrum determines the…
Let $X$ be a vector field and $Y$ be a co-vector field on a smooth manifold $M$. Does there exist a smooth Riemannian metric $g_{\alpha \beta}$ on $M$ such that $Y_\beta = g_{\alpha \beta} X^\alpha$? The main result of this note gives…
We study desingularization of steady vortex rings in three-dimensional axisymmetric incompressible Euler fluids with swirl. Using the variational method, we construct a two-parameter family of steady vortex rings, which constitute a…
Real band topology often appears in systems with space-time inversion symmetry and is characterized by invariants such as the Euler and second Stiefel-Whitney classes. Here, we examine the generic band topology of Bogoliubov de-Gennes (BdG)…
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…
We continue the work started in part I (q-alg/9706004) and prove the invariance and universality in the class of finite type invariants of the object defined and motivated there, namely the Aarhus integral of rational homology 3-spheres.…
This paper is concerned with the helicity associated to solutions of the 3D incompressible Euler equations. We show that under mild conditions on the regularity of the velocity field of an incompressible ideal fluid it is possible to define…
Based on the mechanics of the Euler equation at short time, we show that a Recent Fluid Deformation (RFD) closure for the vorticity field, neglecting the early stage of advection of fluid particles, allows to build a 3D incompressible…
We study the use of the Euler characteristic for multiparameter topological data analysis. Euler characteristic is a classical, well-understood topological invariant that has appeared in numerous applications, including in the context of…
The group SU(3) is parameterized in terms of generalized ``Euler angles''. The differential operators of SU(3) corresponding to the Lie Algebra elements are obtained, the invariant forms are found, the group invariant volume element is…
In this paper, we uncover an intriguing algebra property of an element symmetric polynomial. By this property, we establish the longtime existence and convergence of a locally constrained flow, thereby some families of geometric…
There is a remarkable and canonical problem in 3D geometry and topology: To understand existing models of 3D fluid motion or to create new ones that may be useful. We discuss from an algebraic viewpoint the PDE called Euler's equation for…
In this article we will introduce a new model to describe the leading order behavior of an ideal and axisymmetric fluid moving in a very narrow domain. After providing a formal derivation of the model, we will prove the well-posedness and…
A new important relation between fluid mechanics and differential geometry is established. We study smooth steady solutions to the Euler equations with the additional property: the velocity vector is orthogonal to the gradient of the…
We study the geodesic flow on the normal line congruence of a minimal surface in ${\Bbb{R}}^3$ induced by the neutral K\"ahler metric on the space of oriented lines. The metric is lorentz with isolated degenerate points and the flow is…