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 \((\mathcal{A}^q (M),\mathop D\limits^ \vee _q )\)related with the G2-structure of M.In this paper we study the cohomology \(\mathop H\limits^ \vee *(M)\) 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\(\mathop H\limits^ \vee *(\Gamma \backslash K)\) of any cocalibrated G2-nilmanifold Γ\K is also studied.
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Fernández, M., Ugarte, L. Dolbeault Cohomology for G2-Manifolds. Geometriae Dedicata 70, 57–86 (1998). https://doi.org/10.1023/A:1004940807017
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DOI: https://doi.org/10.1023/A:1004940807017