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 AdS 3 ) and constant torsion provide exact solutions.

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 firstorder 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 AdS3) and constant torsion provide exact solutions.

We discuss locally Weyl (scale) covariant generalisation of quadratic curvature gravity theory in three dimensions using Riemann-Cartan-Weyl space-times. We show that this procedure of Weyl gauging yields a consistent generalisation for a particular class of quadratic curvature gravity theories which includes the New Massive Gravity theory.

No abstract

We discuss the formulation of cosmological topologically massive (simple) supergravity theory in three‐dimensional Riemann‐Cartan space‐times. We use the language of exterior differential forms and the properties of Majorana spinors on 3‐dimensional space‐times to explicitly demonstrate the local supersymmetry of the action density involved. Exact coupled field equations that are complete in both of their bosonic and fermionic sectors are derived by a first order variational principle subject to a torsion‐constraint imposed by the method of Lagrange multipliers. Cotton and Cottino 2‐forms that are complete to all orders in the gravitino field are derived and their properties such as trace are investigated.