ON SL (3, R)-ACTIONS ON 4-SPHERES

摘要

We construct a natural, continuous SL(3, R)-action on S~4 which is an extension of the SO(3)-ac-tion ψ of Uchida. The construction is based on the Kuiper theorem asserting that the quotient space of CP(2) by complex conjugation is S~4. We also give a new proof of the Kuiper theorem.