The effective sigma-model of multidimensional gravity
  The properties of the effective sigma-model for D-dimensional Einstein gravity based on multidimensional geometries is analyzed. Besides pure geometry, additional minimally coupled scalars and (p+2)-forms are considered which yield an extended target space after reduction to the effective D_0-dimensional geometry.   In any case the target space is a homogeneous space. The orthobrane condition guarantees the existence of exact solutions. Geometrically, it makes the target space a locally symmetric one.   New solutions with scalar fields are found, which may inflate not only in time-like but in also in additional spatial directions of the effective geometry.   Static spherically symmetric solutions with a particular configuration of intersecting electric and magnetic branes are investigated both, for the orthobrane case and for degenerated charges. In both cases T_H depends critically on the intersection dimension of the p-branes.   Finally, the role of the Einstein frame for 4-geometries is addressed, and the physical frame transformation for cosmological geometries is given. 
M. Rainer