Homogeneous Kähler structures on principal R^×-bundles reduce to Sasakian structures exactly when the Euler vector field is pre-geodesic and the line bundle is oriented, and the same dictionary covers co-Kähler structures as the 'invariant' case.
Homogeneous G-structures
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
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.
citation-role summary
background 1
citation-polarity summary
fields
math.DG 1years
2026 1verdicts
CONDITIONAL 1roles
background 1polarities
unclear 1representative citing papers
citing papers explorer
-
On Homogeneous K\"ahler Manifolds
Homogeneous Kähler structures on principal R^×-bundles reduce to Sasakian structures exactly when the Euler vector field is pre-geodesic and the line bundle is oriented, and the same dictionary covers co-Kähler structures as the 'invariant' case.