2005/12/10 by Ryushi Goto, Goto, Ryushi · 1 citation
Mathematics · Physics and Astronomy · #53C15 #53C25 #Advanced Algebra and Geometry #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #math.DG #msc:53C15 #msc:53C25
paper · pdf · doi:10.48550/arxiv.math/0512211
AMS-TeX, 38pages
arxiv created 2005/12/10 · openalex publication_date 2005/12/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we will introduce a new notion of geometric structures defined by systems of closed differential forms in term of the Clifford algebra of the direct sum of the tangent bundle and the cotangent bundle on a manifold. We develop a unified approach of a deformation problem and establish a criterion of unobstructed deformations of the structures from a cohomological point of view. We construct the moduli spaces of the structures by using the action of b-fields and show that the period map of the moduli space is locally injective under a cohomological condition (the local Torelli type theorem). We apply our approach to generalized Calabi-Yau (metrical) structures and obtain an analog of the theorem by Bogomolov-Tian-Todorov. Further we prove that deformations of generalized Spin(7) structures are unobstructed.