Homogeneous G-structures

Abstract

The theory of $G$-structures provides us with a unified framework for a large class of geometric structures, including symplectic, complex and Riemannian structures, as well as foliations and many others. Surprisingly, contact geometry - the "odd-dimensional counterpart" of symplectic geometry - does not fit naturally into this picture. In this paper, we introduce the notion of a homogeneous $G$-structure, which encompasses contact structures, as well as some other interesting examples that appear in the literature.

arXiv comment20 pages, to appear in Ann. Mat. Pura Appl., comments welcome

References in corpus (5)

• Symplectic and Poisson geometry on b-manifolds
• A survey on cosymplectic geometry
• Remarks on Contact and Jacobi Geometry
• Holomorphic Jacobi Manifolds and Holomorphic Contact Groupoids
• The Local Structure of Generalized Contact Bundles