Real Submanifolds and Holomorphic Mappings in Several Complex Variables

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9704835 Gong This project aims to understand structures and invariants of real submanifolds in complex spaces. The investigator is to study a class of totally real embeddings of real manifolds in the complex Euclidean space which satisfy a certain second order differential relation. He is to investigate the global topological property of such embeddings and the relationship between the complex tangency of real submanifolds and the singularity arising from the structure of real submanifolds with respect to the holomorphic volume form on the complex Euclidean space. Submanifolds are higher dimensional analogs of surfaces in space; complex spaces are generalizations of real spaces based on complex numbers. Real submanifolds in complex spaces are interesting in that they exhibit both real and complex number based characteristics. They also arise as the boundaries of domains of holomorphy, meaning that they bound regions on which a rather special class of complex-valued functions can be defined.