Contact Topology and Hydrodynamics Iii: Knotted Orbits
نویسندگان
چکیده
We employ the relationship between contact structures and Beltrami fields derived in part I of this series to construct a steady nonsingular solution to the Euler equations on a Riemannian S whose flowlines trace out closed curves of all possible knot and link types. Using careful contact-topological controls, we can make such vector fields realanalytic and transverse to the tight contact structure on S. Sufficient review of concepts is included to make this paper independent of the previous works in this series.
منابع مشابه
Contact Topology and Hydrodynamics Ii: Solid Tori
We prove the existence of periodic orbits for steady realanalytic Euler flows on all Riemannian solid tori. By using the correspondence theorem from part I of this series, we reduce the problem to the Weinstein Conjecture for solid tori. We prove the Weinstein Conjecture on the solid torus via a combination of results due to Hofer et al. and a careful analysis of tight contact structures on sol...
متن کاملCONTACT TOPOLOGY AND HYDRODYNAMICS I: Beltrami fields and the Seifert Conjecture
We draw connections between the field of contact topology (the study of totally nonintegrable plane distributions) and the study of Beltrami fields in hydrodynamics on Riemannian manifolds in dimension three. We demonstrate an equivalence between Reeb fields (vector fields which preserve a transverse nowhere-integrable plane field) up to scaling and rotational Beltrami fields (nonzero fields pa...
متن کاملContact Topology and Hydrodynamics
We draw connections between the field of contact topology and the study of Beltrami fields in hydrodynamics on Riemannian manifolds in dimension three. We demonstrate an equivalence between Reeb fields (vector fields which preserve a transverse nowhere-integrable plane field) up to scaling and rotational Beltrami fields on three-manifolds. Thus, we characterise Beltrami fields in a metric-indep...
متن کاملFolding Pathways of a Knotted Protein with a Realistic Atomistic Force Field
We report on atomistic simulation of the folding of a natively-knotted protein, MJ0366, based on a realistic force field. To the best of our knowledge this is the first reported effort where a realistic force field is used to investigate the folding pathways of a protein with complex native topology. By using the dominant-reaction pathway scheme we collected about 30 successful folding trajecto...
متن کاملOrbit Spaces Arising from Isometric Actions on Hyperbolic Spaces
Let be a differentiable action of a Lie group on a differentiable manifold and consider the orbit space with the quotient topology. Dimension of is called the cohomogeneity of the action of on . If is a differentiable manifold of cohomogeneity one under the action of a compact and connected Lie group, then the orbit space is homeomorphic to one of the spaces , , or . In this paper we suppo...
متن کامل