Radu Slobodeanu

On the geometrized Skyrme and Faddeev models

Abstract The higher power derivative terms involved in both Faddeev and Skyrme energy functionals correspond to σ 2 -energy, introduced by Eells and Sampson (1964) [1] . This paper provides a detailed study of the first and second variation formulae associated to this energy. Some classes of (stable) critical points are outlined.

PERFECT FLUIDS FROM HIGH POWER SIGMA-MODELS

Certain critical points of a sextic sigma-model Lagrangian reminiscent of Skyrme model correspond to perfect fluids with stiff matter equation of state. We analyze from a differential geometric perspective this correspondence extended to general barotropic fluids.

A special class of holomorphic mappings and the Faddeev-Hopf model

Abstract Pseudo horizontally weakly conformal maps [16] extend both holomorphic and (semi)conformal maps into an almost Hermitian manifold. We find critical points for the (generalized) Faddeev-Hopf model [28] in this larger class.

Shear-free perfect fluids with linear equation of state

We prove that shear-free perfect fluid solutions of Einstein?s field equations must be either expansion-free or rotation-free (as conjectured by Ellis and Treciokas) for all linear equations of state p = w? except for .

PSEUDO-HARMONIC MORPHISMS WITH LOW DIMENSIONAL FIBERS

Harmonic morphisms with one-dimensional fibers are subject to various classification results [6], [13]. Motivated by this fact, we point out some particular phenomena which occur in the case ofpseudo-harmonic morphisms with one and two-dimensional fibers.

ON A STABILITY PROPERTY OF SKYRME-RELATED ENERGY FUNCTIONALS

We study the stability of critical maps from (or into) spheres with respect to the symplectic Dirichlet and

Shear-free perfect fluids with a barotropic equation of state in general relativity: the present status

\sigma_2

Steady Euler flows and the Faddeev-Skyrme model with mass term

energies which are the fourth power terms in Skyrme type sigma-models.

A Characterization of Dirac Morphisms

The present status of the shear-free fluid conjecture in general relativity is discussed: a review is given of recent partial proofs, a new and complete proof is given for the case of a linear equation of state, including a non-zero cosmological constant, and a number of useful results are presented which might help in proving the conjecture for a general equation of state.

Holomorphicity and the Walczak formula on Sasakian manifolds

We point out a duality between integrable (in an appropriate sense) steady incompressible Euler flows and the solutions of the strongly coupled Faddeev-Skyrme sigma model with a potential term. We supplement this result with various applications and several explicit classical solutions.