Generalized geometry (in Hitchin's sense, following Courant and Dorfman) is adapted to the physical motion of string-like particles in the same way that traditional geometry is adapted to the physical motion of point-like particles. More general generalized geometries are useful in connection with higher dimensional objects such as membranes (and hence also M-theory). Pavol Severa's first letter to Alan Weinstein is a nice early reference point for the basic idea.
David MJC
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