New improved massive gravity and three-dimensional spacetimes of constant curvature and constant torsion

We derive the field equations for topologically massive gravity coupled with the most general quadratic curvature terms using the language of exterior differential forms and a first order constrained variational principle. We find variational field equations both in the presence and absence of torsion. We then show that spaces of constant negative curvature (i.e. the anti–de Sitter space ${\mathrm{AdS}}_3$) and constant torsion provide exact solutions.