TORSION AND WEYL CONVECTOR IN METRIC-AFFINE MODELS OF GRAVITY

In this work, we analyze the projective transformations of nonlinear c urvature scalar Lagrangians and show that only the Weyl covector piece of the nonmetricity and the vector part of the torsion are affected b y these transformations in an opposite manner. It is pointed out that, since the Dirac equation couples only to the axial piece of the torsi on, it is projectively invariant. Moreover, we look at a generalized t opological 3D gravity by supplementing a translational Chern-Simons te rm. We obtain an exact solution, with a conformal de Sitter background which implys that, for very large times, Poincare invariance becomes exact. (C) 1995 American Institute of Physics.