The relativistic optics of the nondispersive media endowed with the metric gij(x) [Eq. (1.6)] and with a nonlinear connection [Eq. (1.2)] is studied. The d-connection [Eqs. (3.3)– (3.4)] relates the conformal and projective properties of the space- time. A post-Newtonian estimation for the metric gij(x) is also given. It is shown that the solar system tests impose a constraint [Eq. (4.20)] on a combination of the post- Newtonian parameters describing the model.

A geometric formulation of the gravitation theory in the spacetime R × S 3 is given. A linear connection is introduced on the tangent bundle T(R × S 3 ) and then the connection coefficients and the Riemann curvature tensor are calculated. It is shown that their expressions differ from those of Carmeli and Malin [Found. Phys.17, 407 (1987)] by supplementary terms due to the noncommutativity of derivatives used on the spacetime R × S 3 . The Einstein field equations (...) are written as usually and a comparison with other results is given. Finally, some observations about a possible gauge theory of gravitation in the spacetime R × S 3 are made. (shrink)

A model for gauge theories over a compact Lie group is described using R × S3 as background space. The U(1) and SU(2) gauge theories are considered as particular examples, and a comparison with other results is given. Our results differ from those of Carmeli and MalinFound. Phys. 16, 791 (1986);17, 193 (1987)] by a supplementary term in the curvature tensor due to the noncommutativity of derivatives used on R × S3 space. Some observations about supersymmetry and gravity on R (...) × S3 space are also given. (shrink)