The kinetic energy and and the geometric structure in the $B=2$ sector of the Skyrme model: A study using the Atiyah-Manton Ansatz

We study the construction of the collective-coordinate manifold in the baryon number two sector of the Skyrme model. To that end we use techniques of adiabatic large amplitude collective motion, which treat potential and kinetic energy on an equal footing. In this paper the starting point is the Ansatz proposed by Atiyah and Manton (Phys.~Lett.~{\bf 438B}, 222 (1989)), which allows a study of the dynamics using a finite and small number of variables. From these variables we choose a subset of collective ones. We then study the behavior of inertial parameters along parts of the collective manifold, and study the dynamical parts of the interaction.