Chern 9504915 A number of projects in the general area of classical and global differential geometry are proposed. In particular, the proposer wants to continue his work in complex projective geometry and Finsler geometry. The project on complex projective geometry emphasizes the holomorphic aspect rather than the more fashionable Kahler aspect; the project on Finsler geometry is in part motivated by Hilbert's 23rd problem. Finsler geometry could become more important as several new applications have been found, for example in control theory. Chern has an impressive track record of reviving old ideas with new applications. Chern's transgression formulae for the Chern-simons characteristic classes have recently found applications in physics. Also, proposed research on geometric transformations relates to soliton theory which is a mathematical theory of solitary waves.
