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Generalized Tanaka prolongation and its applications

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TWT - Twistor theory

Given a subset of the Douady space of a complex manifold, the total spaceof the universal family has a natural geometric structure induced from the double fibration,a pseudo-product structure. We consider geometric conditions, ensuring thatthis structure has finite-dimensional prolongation. Under these conditions, we showthat there is a canonical absolute parallelism on a suitable fiber space. To do thiswe formulate and prove a generalized version of Tanaka’s prolongation procedure forgeometric structures of nonconstant symbol. This is joint work with Jun-Muk Hwang.

This talk is part of the Isaac Newton Institute Seminar Series series.

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