To appear in Comm. Contemp. Math. GERBES, HOLONOMY FORMS AND REAL STRUCTURES
نویسنده
چکیده
We study geometry on real gerbes in the spirit of CheegerSimons theory. The concepts of adaptations and holonomy forms are introduced for flat connections on real gerbes. Their relations to complex gerbes with connections are presented, as well as results in loop and map
منابع مشابه
Gerbes, Holonomy Forms and Real Structures
We study geometry on real gerbes in the spirit of CheegerSimons theory. The concepts of adaptations and holonomy forms are introduced for flat connections on real gerbes. Their relations to complex gerbes with connections are presented, as well as results in loop and map
متن کاملQuaternionic Kähler and Spin(7) Metrics Arising from Quaternionic Contact Einstein Structures
We construct left invariant quaternionic contact (qc) structures on Lie groups with zero and non-zero torsion and with non-vanishing quaternionic contact conformal curvature tensor, thus showing the existence of non-flat quaternionic contact manifolds. We prove that the product of the real line with a seven dimensional manifold, equipped with a certain qc structure, has a quaternionic Kähler me...
متن کاملOn the Lifts of Minimal Lagrangian Submanifolds
Bryant and Salamon constructed metrics with holonomy G2 and Spin(7) on spin bundles of 3-dimensional space forms, and spin bundles and bundles of anti-self-dual 2-forms on self-dual Einstein 4-manifolds [BrS]. Since, apart from holonomy, the construction of integrable G2(respectively Spin(7)) structures amounts to finding differential 3(4)forms of generic type on 7(8) manifolds satisfying appro...
متن کاملHalf-flat nilmanifolds
We introduce a double complex that can be associated to certain Lie algebras, and show that its cohomology determines an obstruction to the existence of a half-flat SU(3)-structure. We obtain a classification of the 6-dimensional nilmanifolds carrying an invariant half-flat structure. MSC classification: Primary 53C25; Secondary 53C29, 17B30 An SU(3)-structure on a manifold of real dimension 6 ...
متن کاملEmbedding into Manifolds with Torsion
We introduce a class of special geometries associated to the choice of a differential graded algebra contained in Λ∗Rn. We generalize some known embedding results, that effectively characterize the real analytic Riemannian manifolds that can be realized as submanifolds of a Riemannian manifold with special holonomy, to this more general context. In particular, we consider the case of hypersurfa...
متن کامل