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This paper focuses on a geometric structure defined by a system of closed exterior differential forms and develops a new approach to deformation problems of geometric structures. We obtain a criterion for unobstructed deformations from a cohomological point of view (Theorem 1.7). Further we show that under a cohomological condition, the moduli space of the geometric structures becomes a smooth manifold of finite dimension (Theorem 1.8). We apply our approach to the geometric structures such as Calabi–Yau, HyperKahler, G2 and Spin(7) structures and then obtain a unified construction of smooth moduli spaces of these four geometric structures. We generalize the Moser's stability theorem to provide a direct proof of the local Torelli type theorem in these four geometric structures (Theorem 1.10).

MODULI SPACES OF TOPOLOGICAL CALIBRATIONS, CALABI–YAU, HYPERKÄHLER, G2 and SPIN(7) STRUCTURES

MODULI SPACES OF TOPOLOGICAL CALIBRATIONS, CALABI–YAU, HYPERKÄHLER, G₂ and SPIN(7) STRUCTURES