The space of conics immersed in a translation surface.

A translation surface is a topological surface (over R) equipped with an atlas such that each transition function is a translation in the plane Such surfaces are fundamental objects in Teichmueller theory. Such surfaces are canonically locally Euclidean and so it makes sense to consider isometric immersions of conic sections (including the `interiors'). We describe the space of such immersions and its relation to the Teichmueller geodesic flow on moduli space.