Abstract: | Cocalibrated G2-manifolds are seven-dimensional Riemannian manifolds with a distinguished 3-form which is coclosed. For such a manifold M, S. Salamon in Riemannian Geometry and Holonomy Groups (Longman, 1989) defined a differential complex
related with the G2-structure of M.In this paper we study the cohomology
of this complex;it is treated as an analogue of a Dolbeault cohomologyof complex manifolds. For compact G2-manifoldswhose holonomy group is a subgroup of G2 special propertiesare proved. The cohomology
of any cocalibrated G2-nilmanifold \K is also studied. |