We give a coordinate-free description of real manifolds occurring in certain
four dimensional supergravity theories with antisymmetric tensor fields. The
relevance of the linear multiplets in the compactification of string and
five-brane theories is also discussed.Comment: 10 pgs (TeX with Harvmac), CERN-TH.7211/94, UCLA/94/TEP/14,
POLFIS-TH.01/9