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

Weyl Covariant Quadratic Curvature Gravity in 3-Dimensional Riemann-Cartan-Weyl Space-Times