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By Lucia Alessandrini, Giovanni Bassanelli (auth.), Prof. Dr. Klas Diederich (eds.)

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Additional info for Complex Analysis: Proceedings of the International Workshop Wuppertal 1990

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One of our results in [TID) is that this description of the new complex structure as a deformation ¢ of the standard complex structure holds on all of C . The circular model for D is the circular domain together with the deformation tensor, denoted by (C, ¢). ) \\'e show that a detailed analysis of these two facts together with the integrability condition for complex structures lead naturally to a complete characterization of the deformation tensors which arise via this process. The basic properties of the tensor ¢ which follow from this analysis can be loosely described as follows: 1.

And as such, it has an exponential map), and is consequently equivariant under biholomorphic maps of pointed framed strongly convex domains. Patrizio [Pfshowed the tiU! map could more appropriately be thought of as a map (which, at risk of confusion, we will still refer to by the same name) iII:Co--+D and that the map is then CIon C := {h < I}. The mapping iII can be used to pull back the complex structure from the domain D to obtain a new integrable complex structure on C. This new complex structure can be expressed as a deformation of the standard complex structure on T"D.

Let [1,a 1 , ••• , a R] be a line in TpD. Let h : TpD ..... IR be the norm for the infinitesimal Kobayashi metric, and let H(w) = log(h«(, w)/1(12). Let the symbols H, H"" H",p etc. represent the function H and its partial derivatives with respect to the w variables evaluated at the line [1, a 1 , ••• , aRlo Let tJ>'" p tJ>'" p( () be the components of the deformation tensor tJ> relative to the coframing {}logh, dw"', dw lli and its dual framing. Then there is pointed framed domain in the same equivalence class such that, after the change of frame = w"' .....

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