## 18 Citations

Typical field lines of Beltrami flows and boundary field line behaviour of Beltrami flows on simply connected, compact, smooth manifolds with boundary

- MathematicsAnnals of Global Analysis and Geometry
- 2021

We characterise the boundary field line behaviour of Beltrami flows on compact, connected manifolds with vanishing first de Rham cohomology group. Namely we show that except for an at most nowhere…

Topological Features Of Inviscid Flows

- Mathematics
- 2001

The Euler equations for an incompressible inviscid fluid in dimension three possess a wealth of topological phenomena woven into the dynamical and geometric properties of the fluid. Focusing first on…

Bi-invariant metric on volume-preserving diffeomorphisms group of a three-dimensional manifold

- Mathematics
- 2014

We show the existence of a weak bi-invariant symmetric nondegenerate 2-form on the volume-preserving diffeomorphism group of a three-dimensional manifold and study its properties. Despite the fact…

TOPOLOGICALLY MASSIVE ABELIAN GAUGE THEORY

- Mathematics
- 2008

We discuss three mathematical structures which arise in topologically massive Abelian gauge theory. First, the Euclidean topologically massive Abelian gauge theory defines a contact structure on a…

Identification of the Configuration Space Kähler Function

- Mathematics
- 2010

There are two basic approaches to quantum TGD. The first approach, which is discussed in this article, is a generalization of Einstein’s geometrization program of physics to an infinitedimensional…

Physics as In nite-dimensional Geometry I : Identi cation of the Con guration Space Kähler Function

- Mathematics
- 2010

There are two basic approaches to quantum TGD. The rst approach, which is discussed in this article, is a generalization of Einstein's geometrization program of physics to an in nite-dimensional…

Physics as Infinite-dimensional Geometry III: Configuration Space Spinor Structure

- Mathematics
- 2010

There are three separate approaches to the challenge of constructing WCW Kahler geometry and spinor structure. The first approach relies on a direct guess of Kahler function. Second approach relies…

TOPOLOGICAL GEOMETRODYNAMICS: AN OVERVIEW

- Physics
- 2018

If I remember correctly, I got the basic idea of Topological Geometrodynamics (TGD) during autumn 1977, perhaps it was October. What I realized was that the representability of physical space-times…

## References

SHOWING 1-10 OF 54 REFERENCES

Contact topology and hydrodynamics: I. Beltrami fields and the Seifert conjecture

- Mathematics
- 2000

We draw connections between the field of contact topology (the study of totally non-integrable plane distributions) and the study of Beltrami fields in hydrodynamics on Riemannian manifolds in…

Contact topology and hydrodynamics III: knotted orbits

- Mathematics
- 2000

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 S3 whose…

Contact Topology and Hydrodynamics

- Mathematics
- 1997

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…

The topology of stationary curl parallel solutions of Euler’s equations

- Mathematics
- 1981

We study the orbit structure of a vector fieldV defined on a three-dimensional Riemannian manifold which satisfiesV ^ curlV=0. Such a vector field represents the velocity of a stationary solution of…

Contact topology and hydrodynamics II: solid tori

- MathematicsErgodic Theory and Dynamical Systems
- 2002

We prove the existence of periodic orbits for steady real-analytic Euler flows on all Riemannian solid tori. By using the correspondence theorem from part I of this series, we reduce the problem to…

Generalized counterexamples to the Seifert conjecture

- Mathematics
- 1996

Using the theory of plugs and the self-insertion construction due to the second
author, we prove that a foliation of any codimension of any manifold can be modified in a
real analytic or…

The singularity analysis for nearly integrable systems: homoclinic intersections and local multivaluedness

- Mathematics
- 1995

The classification of tight contact structures on the 3-torus

- Mathematics
- 1997

A contact structure £ on a 3-manifold M is called tight if the characteristic foliation of any embedded disc D has no limit cycle, and £ is called overtwisted if otherwise. The classification of over…