Left-invariant grauert tubes on SU(2)

On Rigidity of Grauert Tubes

Given a real-analytic Riemannian manifold M there exists a canonical complex structure on part of its tangent bundle which turns leaves of the Riemannian foliation on TM into holomorphic curves. A Grauert tube over M of radius r, denoted as T rM , is the collection of tangent vectors of M of length less than r equipped with this canonical complex structure. We say the Grauert tube T rM is rigid...

The Geometry of Grauert Tubes and Complexification of Symmetric Spaces

We study the canonical complexifications of non-compact Riemannian symmetric spaces by the Grauert tube construction. We determine the maximal such complexification, a domain already constructed by Akhiezer and Gindikin [1], and show that this domain is Stein. We also determine when invariant complexifications, including the maximal one, are Hermitian symmetric. This is expressed simply in term...

Symplectic Geometry and the Uniqueness of Grauert tubes

Given a differentiable manifold M , it is always possible to find an almost complex structure J on TM with respect to which the zero-section is totally-real. In this paper we study a situation in which there is a canonical choice for a complex structure with this property, a canonical complexification of M . Suppose that (M, g) is a real-analytic Riemannian manifold of dimension n. Identify M w...

Topologically Left Invariant Mean on Dual Semigroup Algebras

On rigidity of Grauert tubes over Riemannian manifolds of constant curvature

It is well-known that a real analytic manifold X admits a complexification XC , a complex manifold that contains X as the fixed point set of an antiholomorphic involution. This can be seen as follows.The transition functions defining the manifold X are real-analytic local diffeomorphisms of Rn. The Taylor expansions of these transition functions can be considered as local biholomorphisms of Cn,...