Locally homogeneous structures on Hopf surfaces

Locally homogeneous rigid geometric structures on surfaces

We study locally homogeneous rigid geometric structures on surfaces. We show that a locally homogeneous projective connection on a compact surface is flat. We also show that a locally homogeneous unimodular affine connection ∇ on a two dimensional torus is complete and, up to a finite cover, homogeneous. Let ∇ be a unimodular real analytic affine connection on a real analytic compact connected ...

Baskets, Espaliers, and Homogeneous Braids

Four constructions of Seifert surfaces—Hopf and arborescent plumbing, basketry, and T-bandword handle decomposition—are described, and some interrelationships expounded, e.g.: arborescent Seifert surfaces are baskets; Hopf-plumbed baskets are precisely homogeneous T-bandword surfaces.

Bihermitian Metrics on Hopf Surfaces

Inspired by a construction due to Hitchin [20], we produce strongly bihermitian metrics on certain Hopf complex surfaces, which integrate the locally conformally Kähler metrics found by Gauduchon–Ornea [14]. We also show that the Inoue complex surfaces with b2 = 0 do not admit bihermitian metrics. This completes the classification of the compact complex surfaces admitting strongly bihermitian m...

Reiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras

Geometric Structures and Varieties of Representations

Many interesting geometric structures on manifolds can be interpreted as structures locally modelled on homogeneous spaces. Given a homogeneous space (X,G) and a manifold M , there is a deformation space of structures on M locally modelled on the geometry of X invariant under G. Such a geometric structure on a manifold M determines a representation (unique up to inner automorphism) of the funda...