Complex contact manifolds and S 1 actions

Remarks on Complex Contact Manifolds

1. Statement of results. Let M be a complex manifold of complex dimension 2w + l. Let { Ui} be an open covering of M. We call M a complex contact manifold if the following conditions are satisfied: (1) On each [/,there exists a holomorphic 1-form w,such that Wi/\(do3i)n is different from zero at every point of Ui. (2) If UiC\Uj is nonempty, then there exists a nonvanishing holomorphic function ...

A Note on Homogeneous Complex Contact Manifolds

A Convexity Theorem for Torus Actions on Contact Manifolds

We show that the image cone of a moment map for an action of a torus on a contact compact connected manifold is a convex polyhedral cone and that the moment map has connected fibers provided the dimension of the torus is bigger than 2 and that no orbit is tangent to the contact distribution. This may be considered as a version of the Atiyah Guillemin Sternberg convexity theorem for torus action...

An equivariant index formula for elliptic actions on contact manifolds

Given an elliptic action of a compact Lie group G on a co-oriented contact manifold (M, E) one obtains two naturally associated objects: A G-transversally elliptic operator Db / , and an equivariant differential form with generalised coefficients J (E, X) defined in terms of a choice of contact form on M . We explain how the form J (E, X) is natural with respect to the contact structure, and gi...

Multiplicity-free Representations and Visible Actions on Complex Manifolds

mulas §1.5. Multiplicity-free representations — definition §2. Multiplicity-free theorem — general framework §2.1. Holomorphic bundles and anti-holomorphic maps §2.2. Multiplicity-free theorem — line bundle case §2.3. Geometry on the base space D §2.4. Multiplicity-free theorem — vector bundle case §3. Visible actions on complex manifolds §3.1. Previsible and visible actions on complex manifold...