On the geometry of Kawaguchi spaces (Q5930986)

First the basic notions of a Kawaguchi space of second order are surveyed and the generalized Kawaguchi space is defined. Then the author proves that the metric function \(F(x,\dot x,\ddot x)\) of a generalized Kawaguchi space \((g.K^n)\) defines a one-parameter bundle of almost quaternionic structures and finds conditions for the complete integrability of these structures. Finally, conditions are found in order that the affine connection of \((g.K^n)\) is associated with the antiquaternionic structure.