CONTACT GEOMETRY IN ELECTROMAGNETISM

Coframe geometry, gravity and electromagnetism

The extensions of GR for description of fermions on a curved space, for supergravity, and for the loop quantum gravity ordinary use a set of 16 independent variables instead of 10 components of metric. These variables can be assembled in a coframe field, i.e., a set of four linearly independent 1-forms. In this presentation we review a geometrical structure based on the coframe field. We constr...

Gravity and Electromagnetism in Noncommutative Geometry

We present a unified description of gravity and electromagnetism in the framework of a Z2 noncommutative differential calculus. It can be considered as a “discrete version” of Kaluza-Klein theory, where the fifth continuous dimension is replaced by two discrete points. We derive an action which coincides with the dimensionally reduced one of the ordinary Kaluza-Klein theory. PACS. 04.20.Jb, 04....

Contact Geometry

2 Contact manifolds 4 2.1 Contact manifolds and their submanifolds . . . . . . . . . . . . . . 6 2.2 Gray stability and the Moser trick . . . . . . . . . . . . . . . . . . 13 2.3 Contact Hamiltonians . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.4 Darboux’s theorem and neighbourhood theorems . . . . . . . . . . 17 2.4.1 Darboux’s theorem . . . . . . . . . . . . . . . . . . . . . . . 17...

Lagrangian intersections in contact geometry

Contact Geometry of Curves

Cartan’s method of moving frames is briefly recalled in the context of immersed curves in the homogeneous space of a Lie group G. The contact geometry of curves in low dimensional equi-affine geometry is then made explicit. This delivers the complete set of invariant data which solves the G-equivalence problem via a straightforward procedure, and which is, in some sense a supplement to the equi...