Correspondence between Jordan-Einstein frames and Palatini-metric
  formalisms
  We discuss the conformal symmetry between Jordan and Einstein frames
considering their relations with the metric and Palatini formalisms for
modified gravity. Appropriate conformal transformations are taken into account
leading to the evident connection between the gravitational actions in the two
mentioned frames and the Hilbert-Einstein action with a cosmological constant.
We show that the apparent differences between Palatini and metric formalisms
strictly depend on the representation while the number of degrees of freedom is
preserved. This means that the dynamical content of both formalism is
identical.
